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A certain university will select 1 of 7 candidates eligible
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11 Mar 2014, 03:27
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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 Problem Solving Question: 151 Category: Arithmetic Elementary combinatorics Page: 82 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: A certain university will select 1 of 7 candidates eligible
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11 Mar 2014, 03:27
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.
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Re: A certain university will select 1 of 7 candidates eligible
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11 Mar 2014, 04:19
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
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Re: A certain university will select 1 of 7 candidates eligible
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11 Mar 2014, 07:27
Bunuel wrote: RESERVED FOR A SOLUTION. 7c1=7 10c2=45 7*45= 315
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Re: A certain university will select 1 of 7 candidates eligible
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08 Jul 2017, 05:22
answer must be E identical positions should be divided by 2 such as 7*10*9/1*2=315



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Re: A certain university will select 1 of 7 candidates eligible
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22 Jun 2018, 07:17
Bunuel wrote: SOLUTION
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
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. Bunuel What is the purpose of the statement " If none of the candidates is eligible for a position in both departments" in the question. Does it have any significance?
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Re: A certain university will select 1 of 7 candidates eligible
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22 Jun 2018, 12:23
So basically, in the first set we have to choose 1 individual out of the 7 in which case the total number of possible choices would be obviously 7.
In the second set we have to choose a combination of 2 individuals out of the 10. I found it easier to visualize this like this: Possible Individuals > A B C D E F G H I J > Each letter represents 1 specific individual Combinations with Person A > AB AC AD AE AF AG AH AI AJ = 9 unique possible combinations Combinations with Person B > BC BC BE BF BG BH BI BJ = 8 unique possible combinations Combinations with Person C > CD CE CF CG CH CI CJ = 7 unique possible combinations and so on...
What the second set will then look like once we have all the possible unique combinations is basically: 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45
Now we just multiply the number of possible choices from set 1 with the unique number of combinations from set 2 and we get: 7 x 45 = 315
The answer is E



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Re: A certain university will select 1 of 7 candidates eligible
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25 Jun 2018, 12:02
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
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Re: A certain university will select 1 of 7 candidates eligible
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04 Aug 2019, 13:33
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



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Re: A certain university will select 1 of 7 candidates eligible
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05 Aug 2019, 08:51
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".
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Re: A certain university will select 1 of 7 candidates eligible
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