It is currently 21 Nov 2017, 21:27

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A certain university will select 1 of 7 candidates eligible

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 27 Aug 2007
Posts: 253

Kudos [?]: 12 [5], given: 0

A certain university will select 1 of 7 candidates eligible [#permalink]

### Show Tags

17 Nov 2007, 06:35
5
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

85% (01:20) correct 15% (01:34) wrong based on 397 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-university-will-select-1-of-7-candidates-eligible-103273.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Dec 2013, 07:20, edited 1 time in total.
Edited the question and added the OA.

Kudos [?]: 12 [5], given: 0

VP
Joined: 08 Jun 2005
Posts: 1143

Kudos [?]: 254 [1], given: 0

### Show Tags

17 Nov 2007, 07:37
1
KUDOS
1C7*2C10 = 7*45 = 315

Kudos [?]: 254 [1], given: 0

VP
Joined: 08 Jun 2005
Posts: 1143

Kudos [?]: 254 [1], given: 0

### Show Tags

17 Nov 2007, 07:58
1
KUDOS
1
This post was
BOOKMARKED
Ferihere wrote:
KillerSquirrel wrote:
1C7*2C10 = 7*45 = 315

the explanation would be greatly appreciated...

To find the ways to choose one item out of a group of items we can use the combinations formula (i.e xCn = n!/((n-x)!*x!)).

So the ways to choose one out of seven is 1C7 = 7!/6!*1! = 7 and two out of ten is 10!/8!*2! = 45.

Total ways for both are ---> 7*45 = 315

Alternatively you can say that:

1/7*2/10*1/9 = 2/630 = 1/315

Kudos [?]: 254 [1], given: 0

Director
Joined: 25 Oct 2008
Posts: 594

Kudos [?]: 1185 [0], given: 100

Location: Kolkata,India
Re: Set #1 (probability question) [#permalink]

### Show Tags

24 Jul 2009, 19:10
7C1X10C2
_________________

http://gmatclub.com/forum/countdown-beginshas-ended-85483-40.html#p649902

Kudos [?]: 1185 [0], given: 100

Manager
Joined: 27 Oct 2008
Posts: 185

Kudos [?]: 166 [0], given: 3

Re: Set #1 (probability question) [#permalink]

### Show Tags

27 Sep 2009, 02:22
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

Soln:
1 out of 7 candidates can be chosen in 7 ways for mathematics department

2 out of 10 candidates can be chosen in 10C2 ways to fill two identical positions in Comp Sci department

Thus total number of ways = 7 * 10C2 = 315

Kudos [?]: 166 [0], given: 3

Senior Manager
Joined: 22 Dec 2009
Posts: 356

Kudos [?]: 419 [1], given: 47

Re: Set #1 (probability question) [#permalink]

### Show Tags

14 Feb 2010, 09:24
1
KUDOS
Ferihere 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

Maths Dept = 7c1 = 7

CS dept = 10c2 = 45

Therefore no of combinations = 7 x 45 = 315 ... E
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!!

|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~

Kudos [?]: 419 [1], given: 47

Manager
Joined: 02 Jan 2010
Posts: 132

Kudos [?]: 6 [0], given: 3

Re: Set #1 (probability question) [#permalink]

### Show Tags

08 Sep 2010, 03:37
damn i think too much...was making a mess of this problem
_________________

Regards
Ganesh
Class of 2012
Great Lakes Institute of Management
http://greatlakes.edu.in

Kudos [?]: 6 [0], given: 3

Manager
Joined: 08 Sep 2010
Posts: 159

Kudos [?]: 28 [0], given: 18

Re: Set #1 (probability question) [#permalink]

### Show Tags

18 Jun 2011, 06:48
agree with 315.. 7c1 * 10c2
_________________

My will shall shape the future. Whether I fail or succeed shall be no man's doing but my own.

If you like my explanations award kudos.

Kudos [?]: 28 [0], given: 18

Senior Manager
Joined: 13 May 2011
Posts: 294

Kudos [?]: 292 [0], given: 11

WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Re: A certain university will select 1 of 7 candidates eligible [#permalink]

### Show Tags

05 Dec 2011, 11:26
(7c1*10c1*9c1)/2! = 315

Kudos [?]: 292 [0], given: 11

Magoosh GMAT Instructor
Joined: 28 Nov 2011
Posts: 303

Kudos [?]: 1263 [8], given: 2

Re: A certain university will select 1 of 7 candidates eligible [#permalink]

### Show Tags

06 Dec 2011, 19:56
8
KUDOS
Expert's post
1
This post was
BOOKMARKED
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(n-1)/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.

_________________

Christopher Lele
Magoosh Test Prep

Kudos [?]: 1263 [8], given: 2

Non-Human User
Joined: 09 Sep 2013
Posts: 15571

Kudos [?]: 283 [0], given: 0

Re: A certain university will select 1 of 7 candidates eligible [#permalink]

### Show Tags

07 Dec 2013, 12:18
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 283 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42281

Kudos [?]: 132984 [1], given: 12400

Re: A certain university will select 1 of 7 candidates eligible [#permalink]

### Show Tags

08 Dec 2013, 07:21
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
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).

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-university-will-select-1-of-7-candidates-eligible-103273.html
_________________

Kudos [?]: 132984 [1], given: 12400

Re: A certain university will select 1 of 7 candidates eligible   [#permalink] 08 Dec 2013, 07:21
Display posts from previous: Sort by