Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 65771

A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
06 Dec 2011, 18:56
Question Stats:
86% (01:37) correct 14% (02:06) wrong based on 1060 sessions
HideShow timer Statistics
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? (A) 42 (B) 70 (C) 140 (D) 165 (E) 315
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 65771

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
11 Mar 2014, 02:27
SOLUTIONA certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?(A) 42 (B) 70 (C) 140 (D) 165 (E) 315 As "none of the candidates is eligible for a position in both departments" then we have 7+10=17 candidates. \(C^1_7*C^2_{10}=7*45=315\): \(C^1_7\)  choosing 1 from 7 and \(C^2_{10}\) choosing 2 from 10 when order doesn't matter as 2 positions in computer science department are identical (XY is the same as YX). Answer: E.
_________________




Intern
Joined: 27 Nov 2011
Posts: 4

I am like those, who find Permutation, combination and probablity a nightmare. However, my short mantra do deal with the easy set is :
Whenever you need to choose or select, use combination
eg: choose/select r from n is: nCr
Whenever you need to choose and order, use combination formula and multiply by with the number you need to order.
eg:Choose/select r from n is: nCr, followed by order of r is nCr*r!



Math Expert
Joined: 02 Sep 2009
Posts: 65771

Avijit wrote: I am like those, who find Permutation, combination and probablity a nightmare. However, my short mantra do deal with the easy set is :
Whenever you need to choose or select, use combination
eg: choose/select r from n is: nCr
Whenever you need to choose and order, use combination formula and multiply by with the number you need to order.
eg:Choose/select r from n is: nCr, followed by order of r is nCr*r! Generally: The words "Permutation" and "Arrangement" are synonymous and can be used interchangeably (order matters). The words "Combination" and "Selection" are synonymous and can be used interchangeably.Check Combinatorics and Probability chapters of Math Book to foind out more on these topics: mathcombinatorics87345.html mathprobability87244.htmlCombinations questions to practice: DS: search.php?search_id=tag&tag_id=31PS: search.php?search_id=tag&tag_id=52Probability questions to practice: DS: search.php?search_id=tag&tag_id=33PS: search.php?search_id=tag&tag_id=54Hard questions on combinations and probability with detailed solutions: hardestareaquestionsprobabilityandcombinations101361.htmlHope it helps.
_________________



Magoosh GMAT Instructor
Joined: 28 Nov 2011
Posts: 300

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
11 Mar 2014, 02:27
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?(A) 42 (B) 70 (C) 140 (D) 165 (E) 315 There are a few possible areas in this problem where you can go wrong. First off: does the solution require combinations or permutations? For the mathematics dept., in which you are selecting 1 person from 7, it is irrelevant whether you use combinations or permutations – the answer is the same. Also, whenever you see nC1, remember that the answer is n (don’t feel you have to set up all the factorials). With the computer science dept., you have two identical positions. Now you have to address the initial question: combinations or permutations. The order in which any two candidates are chosen (say, candidate A and candidate B) is irrelevant (AB is the same as BA) thus you should use the combinations formula. 10C2. The quick math in this case is as follows: when you have nC2, where n is any integer greater than or equal to 4, multiply n(n1)/2 to get the answer. In this case n = 10 so (10)(9)/2 = 45. The second trouble spot is whether to add or multiple the 45 and the 7. Because each of the 7 math departments can be matched up with any 45 of the comp. sci. dept., you want to multiply. The 7 different possibilities for group A can be matched up with the 45 different possibilities from Group B to get: 7 x 45 = 315. Hope that was helpful
_________________



Director
Joined: 25 Apr 2012
Posts: 633
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
11 Mar 2014, 03:19
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
(A) 42 (B) 70 (C) 140 (D) 165 (E) 315
Sol: 1 out of 7 candidates will be selected in 7!/6! or 7 ways 2 out of 10 candidates can be selected by 10!/8!*2! or 45 ways No. of ways in which 3 different sets can be filled is =45*7 =315 Ans is E
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11394
Location: United States (CA)

Re: A certain university will select 1 of 7 candidates eligible
[#permalink]
Show Tags
22 May 2017, 17:57
SoniaSaini wrote: A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
A. 42 B. 70 C. 140 D. 165 E. 315 1 of 7 candidates can fill the math position in 7C1 = 7 ways. 2 of 10 candidates can fill the computer science position in 10C2 = (10 x9)/2! = 45 ways. Thus, the total number of ways to fill the positions is 7 x 45 = 315 ways. Answer: E
_________________
★
★
★
★
★
250 REVIEWS
5STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE
NOW WITH GMAT VERBAL (BETA)
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11394
Location: United States (CA)

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
25 Jun 2018, 11:02
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionA certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? (A) 42 (B) 70 (C) 140 (D) 165 (E) 315 1 of 7 candidates can fill the math position in 7C1 = 7 ways. 2 of 10 candidates can fill the two computer science positions in 10C2 = 10!/(2! x 8!) = (10 x 9)/2! = 45 ways. Thus, the total number of ways to fill the three positions is 7 x 45 = 315. Answer: E
_________________
★
★
★
★
★
250 REVIEWS
5STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE
NOW WITH GMAT VERBAL (BETA)
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



Manager
Joined: 01 Jan 2019
Posts: 107
Location: Canada
Concentration: Finance, Entrepreneurship
GPA: 3.24

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
04 Aug 2019, 12:33
ScottTargetTestPrep wrote: Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionA certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? (A) 42 (B) 70 (C) 140 (D) 165 (E) 315 1 of 7 candidates can fill the math position in 7C1 = 7 ways. 2 of 10 candidates can fill the two computer science positions in 10C2 = 10!/(2! x 8!) = (10 x 9)/2! = 45 ways. Thus, the total number of ways to fill the three positions is 7 x 45 = 315. Answer: E Hi, Can this be done by adding the total candidates as well as the position? I.e. 17 candidates and 3 positions will give 17C3? Just curious Posted from my mobile device



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11394
Location: United States (CA)

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
05 Aug 2019, 07:51
Shef08 wrote: ScottTargetTestPrep wrote: Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionA certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? (A) 42 (B) 70 (C) 140 (D) 165 (E) 315 1 of 7 candidates can fill the math position in 7C1 = 7 ways. 2 of 10 candidates can fill the two computer science positions in 10C2 = 10!/(2! x 8!) = (10 x 9)/2! = 45 ways. Thus, the total number of ways to fill the three positions is 7 x 45 = 315. Answer: E Hi, Can this be done by adding the total candidates as well as the position? I.e. 17 candidates and 3 positions will give 17C3? Just curious Posted from my mobile deviceNo because we are filling positions in "specific departments".
_________________
★
★
★
★
★
250 REVIEWS
5STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE
NOW WITH GMAT VERBAL (BETA)
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



Manager
Joined: 09 Jun 2019
Posts: 105

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
27 Oct 2019, 02:09
Hi ScottTargetTestPrep Could you help me with my query? Quote: If none of the candidates is eligible for a position in both departments What role does this phrase play in the question? Does it affect our calculation at all? Thank you, Dablu



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11394
Location: United States (CA)

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
30 Oct 2019, 16:44
gurudabl wrote: Hi ScottTargetTestPrep Could you help me with my query? Quote: If none of the candidates is eligible for a position in both departments What role does this phrase play in the question? Does it affect our calculation at all? Thank you, Dablu The fact that none of the candidates is eligible for both departments play a significant role in the question. To compare, suppose that there was one person who is eligible for a position in both departments. First of all, since that one person is included both in the 7 candidates for the math department and 10 candidates for the CS department, there are no longer 17 total candidates; there are only 7 + 10  1 = 16 total candidates. Further, the number of sets of 3 candidates change as well. For the math position, we still have 7 choices; however, the number of ways we can fill the CS position depends on whether the person filling the math position is the one eligible for both positions or not. If it is, then there are only 9 people you can choose from to fill the CS position; so in this scenario, the number of ways to choose 2 people from a total of 9 people is 9C2 = 9!/(2!*7!) = (9*8)/2 = 36. On the other hand, if the person chosen for the math department is one of the remaining six people, then we can fill the CS positions by choosing 2 people from a total of 10 people, which can be done in 10C2 = 45 ways, as calculated before. Thus, when there's one person eligible for both positions, the number of ways to fill the three positions is 36 + 6*45 = 306. If you're curios what happened to the 315  306 = 9 ways to fill the three positions, let X be the person eligible for both positions. Since X is included in both the 7 and 10 people, the choices X + XA, X + XB, ... are no longer possible, where A, B, ... denote the people eligible for the CS department besides X. As there are 9 people eligible for the CS department besides X, the total number of ways is reduced by 9.
_________________
★
★
★
★
★
250 REVIEWS
5STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE
NOW WITH GMAT VERBAL (BETA)
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



Manager
Joined: 09 Jun 2019
Posts: 105

A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
30 Oct 2019, 23:19
Hi ScottTargetTestPrep Thank you for replying great explanation! Quote: If you're curios what happened to the 315  306 = 9 ways to fill the three positions, let X be the person eligible for both positions. I totally got this approach: The total no of possible combinations  9 combinations with are not possible Sorry for bothering again, could tell me how did you deduce this? Quote: Thus, when there's one person eligible for both positions, the number of ways to fill the three positions is 36 + 6*45 = 306 When tried solving it directly I got this: let X be the person eligible for both positions. 1st case: If X is selected in Math department 7C1 and 9C2 or 2nd case: If X is selected in CS department. 10C2 and 6C1 = 7C1 * 9C2 + 10C2 * 6C1 = 252 + 270 = 522. Where am I going wrong? Thank you, Dablu



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11394
Location: United States (CA)

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
04 Nov 2019, 18:56
gurudabl wrote: Hi ScottTargetTestPrep Thank you for replying great explanation! Quote: If you're curios what happened to the 315  306 = 9 ways to fill the three positions, let X be the person eligible for both positions. I totally got this approach: The total no of possible combinations  9 combinations with are not possible Sorry for bothering again, could tell me how did you deduce this? Quote: Thus, when there's one person eligible for both positions, the number of ways to fill the three positions is 36 + 6*45 = 306 When tried solving it directly I got this: let X be the person eligible for both positions. 1st case: If X is selected in Math department 7C1 and 9C2 or 2nd case: If X is selected in CS department. 10C2 and 6C1 = 7C1 * 9C2 + 10C2 * 6C1 = 252 + 270 = 522. Where am I going wrong? Thank you, Dablu The only mistake in your calculations is that when X is selected for the position in the Math department, there are not 7C1 = 7 choices; since we are considering the case when X is already selected, the number of ways to fill the position in the Math department is 1C1 = 1. Thus, it should have been 1C1 * 9C2 + 6C1 * 10C2 = 1 * 36 + 6 * 45 = 36 + 270 = 306.
_________________
★
★
★
★
★
250 REVIEWS
5STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE
NOW WITH GMAT VERBAL (BETA)
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



Manager
Joined: 09 Jun 2019
Posts: 105

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
04 Nov 2019, 21:20
Got it Thank you ScottTargetTestPrep! Although, we digressed from the main question this provided me a lot of insight. Thank you again!



CEO
Joined: 03 Jun 2019
Posts: 3339
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
05 Nov 2019, 09:20
Bunuel wrote: A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
(A) 42 (B) 70 (C) 140 (D) 165 (E) 315 Different sets = 7C1 * 10C2 = 7*45= 315 IMO E Posted from my mobile device
_________________
Kinshook Chaturvedi Email: kinshook.chaturvedi@gmail.com



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11394
Location: United States (CA)

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
05 Nov 2019, 18:19
gurudabl wrote: Got it Thank you ScottTargetTestPrep! Although, we digressed from the main question this provided me a lot of insight. Thank you again! Sure thing!
_________________
★
★
★
★
★
250 REVIEWS
5STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE
NOW WITH GMAT VERBAL (BETA)
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



Manager
Joined: 21 Aug 2019
Posts: 132

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
26 Mar 2020, 13:02
ScottTargetTestPrep wrote: Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionA certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? (A) 42 (B) 70 (C) 140 (D) 165 (E) 315 1 of 7 candidates can fill the math position in 7C1 = 7 ways. 2 of 10 candidates can fill the two computer science positions in 10C2 = 10!/(2! x 8!) = (10 x 9)/2! = 45 ways. Thus, the total number of ways to fill the three positions is 7 x 45 = 315. Answer: E Can we solve like this? 7C1 * 10P2 ? I am getting the same answer
_________________
I don't believe in giving up!



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11394
Location: United States (CA)

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
30 Mar 2020, 10:46
gurudabl wrote: Got it Thank you ScottTargetTestPrep! Although, we digressed from the main question this provided me a lot of insight. Thank you again! Sure thing!
_________________
★
★
★
★
★
250 REVIEWS
5STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE
NOW WITH GMAT VERBAL (BETA)
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



Intern
Joined: 18 Jun 2020
Posts: 1

Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
Show Tags
25 Jul 2020, 08:59
ChrisLele wrote: A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?(A) 42 (B) 70 (C) 140 (D) 165 (E) 315 There are a few possible areas in this problem where you can go wrong. First off: does the solution require combinations or permutations? For the mathematics dept., in which you are selecting 1 person from 7, it is irrelevant whether you use combinations or permutations – the answer is the same. Also, whenever you see nC1, remember that the answer is n (don’t feel you have to set up all the factorials). With the computer science dept., you have two identical positions. Now you have to address the initial question: combinations or permutations. The order in which any two candidates are chosen (say, candidate A and candidate B) is irrelevant (AB is the same as BA) thus you should use the combinations formula. 10C2. The quick math in this case is as follows: when you have nC2, where n is any integer greater than or equal to 4, multiply n(n1)/2 to get the answer. In this case n = 10 so (10)(9)/2 = 45.The second trouble spot is whether to add or multiple the 45 and the 7. Because each of the 7 math departments can be matched up with any 45 of the comp. sci. dept., you want to multiply. The 7 different possibilities for group A can be matched up with the 45 different possibilities from Group B to get: 7 x 45 = 315. Hope that was helpful Can you please help me understand this bit  "The quick math in this case is as follows: when you have nC2, where n is any integer greater than or equal to 4, multiply n(n1)/2 to get the answer. In this case n = 10 so (10)(9)/2 = 45." When we pick 3 from 10 for example, the formula yields 30, when it should be 120 as per the factorial formula. How exactly does the above work? Thanks in advance!




Re: A certain university will select 1 of 7 candidates eligible to fill a
[#permalink]
25 Jul 2020, 08:59




