Problem Solving

subh2273 wrote:A group of medical interns at Bohemus Medical School want to go on dates. There are 5
girls and 5 guys. Assuming girls go on dates with guys, how many possible ways can these
10 medical interns date each other?

(A)
10

(B)
25

(C)
60

(D)
90

(E)
120

Take the task of arranging dates and break it into stages.

Let A, B, C, D and E represent the 5 girls

Stage 1: Select a boy to date girl A
We can choose any of the 5 boys, so we can complete stage 1 in 5 ways

Stage 2: Select a boy to date girl B
Since we already selected a boy in stage 1, there are 4 boys remaining to choose from.
So we can complete stage 2 in 4 ways

Stage 3: Select a boy to date girl C
There are 3 boys remaining to choose from.
So we can complete stage 3 in 3 ways

Stage 4: Select a boy to date girl D
2 boys remaining. So we can complete stage 4 in 2 ways

Stage 5: Select a boy to date girl E
There is 1 boy remaining to be seated, so we can complete stage 5 in 1 way

By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus arrange all dates) in (5)(4)(3)(2)(1) ways (= 120 ways)

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- ... /video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should ... 67256.html
- https://www.beatthegmat.com/counting-pr ... 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


MEDIUM
- https://www.beatthegmat.com/combinatori ... 73194.html
- https://www.beatthegmat.com/arabian-hor ... 50703.html
- https://www.beatthegmat.com/sub-sets-pr ... 73337.html
- https://www.beatthegmat.com/combinatori ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-se ... 71047.html
- https://www.beatthegmat.com/combinatori ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p ... 71001.html
- https://www.beatthegmat.com/permutation ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladi ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent

subh2273 wrote:A group of medical interns at Bohemus Medical School want to go on dates. There are 5
girls and 5 guys. Assuming girls go on dates with guys, how many possible ways can these
10 medical interns date each other?

(A)
10

(B)
25

(C)
60

(D)
90

(E)
120

The first girl has 5 choices of guys, the second girl has 4 choices of guys (after a guy is picked by the first girl), the third girl has 3 choices of guys (after a guy is picked by the second girl), and so on. So the number of ways these 10 interns can date each other is 5 x 4 x 3 x 2 x 1 = 120.

Answer: E