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Permutations and Combination

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by BTGmoderatorRO » Fri Dec 29, 2017 8:33 am
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

OA is B

OA says B but I got C please an Expert should help with a breakdown. Thanks.
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by Brent@GMATPrepNow » Fri Dec 29, 2017 8:46 am
Roland2rule 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

OA is B

OA says B but I got C please an Expert should help with a breakdown. Thanks.
We can take the task of filling both positions and break it into stages.

Stage 1: Fill the 1 math position
There are 7 candidates, so we can complete stage 1 in 7 ways

Stage 2: Fill the 2 computer science positions
Note that the order in which we select candidates doesn't matter. For example, selecting candidate B and then candidate C is the same as selecting candidate C and then candidate B. So, we can use combinations here.
We can select 2 candidates from 10 in 10C2 ways (= 45 ways)

Aside: If anyone is interested, we have a free video on calculating combinations (like 10C2) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus fill the three positions in (7)(45) ways ([spoiler]= 315 ways[/spoiler])

Answer: E
--------------------------

Note: the FCP can be used to solve the majority of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html
- https://www.beatthegmat.com/mouse-pellets-t274303.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/ps-counting-t273659.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/please-solve ... 71499.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/laniera-s-co ... 15764.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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