A group of medical interns at Bohemus Medical School want to go on dat

Question

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

(A) 10
(B) 25
(C) 60
(D) 90
(E) 120

Divyadisha · Answer

1st girl can go with 5 guys 
2nd girl can go with remaining 4 
3rd girl can go with remaining 3 and so on

so the total ways are 5!= 120

E should be the answer

Abhishek009 · Answer

5P5 = 120
  
Answer will be (E)

BrentGMATPrepNow · Answer

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. So, be sure to learn it.

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Sammy599 · Answer

The first girl can go on a date in 5 ways.
The second can go on a date in 4 ways.
The third in 3 and so on.

This is equal to 5! i.e. 120.

Hence, the answer should be (E).

I would appreciate a kudos if you liked my solution!

gmathopeful19 · Answer

Because they are all straight, there are five pairs possible.

Total arrangements of these pairs:
5! = 120

Posted from my mobile device

fskilnik · Answer

?\,\,\,\,:\,\,\,\,\# \,\,\,{	ext{guy - girl}}\,\,{	ext{pairs}}

Imagine girls in a row (say) in alphabetical order.

FOCUS: number of ways to put 5 guys in a row (parallel to the first row, each guy facing one girl - this is a pair!)

?\, = \,{P_{\,5}}\,\, = 5! = 120

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

ScottTargetTestPrep · Answer

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

silence_13 · Answer

The question says "Assume girls go on dates with boys" but it doesn't say otherwise i.e. there is no assumption about boys going on dates with girls only. I'm wondering if the question could be worded better - as the possibility of boys going on dates with boys can increase the number of ways in which the interns can date each other.

iamyogi25 · Answer

Hello... I see this is like slot problem and see lots of explanations like 1 person has 5 options, then the next will have 4 and so on. So, 5!. Here is my question, why are we restricting it? For example, is it assumed once somebody is chosen, then you can not reuse it? My query is coming from the scenerio- say there are 5 teams in group A and 5 in group B, they have to play the other group and only once then we say it is 5*5 matches or say another scenerio, when you have total of 10 teams in one league and they have to play each other once then it becomes simply 10C2. Going back to original question: why are we not saying second person also has 5 choices and so on? Sorry for deviating from the original question. Just wanted to understand what is going on? Thank you in advance

Bunuel

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

Bunuel · Answer

Do not overcomplicate. The question means all 10 people are dating at the same time, with each girl paired with exactly one guy and each guy used once. It is not about one boy choosing a girl independently. Once a guy is paired, he is unavailable to others. That is exactly why the count is the number of one-to-one pairings, which is 5!.

iamyogi25 · Answer

As always thank you, Bunuel.

A group of medical interns at Bohemus Medical School want to go on dat

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