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

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A group of medical interns at Bohemus Medical School want to go on dat  [#permalink]

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02 Jun 2016, 04:41
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Difficulty:

55% (hard)

Question Stats:

53% (01:20) correct 47% (01:09) wrong based on 141 sessions

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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

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Re: A group of medical interns at Bohemus Medical School want to go on dat  [#permalink]

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02 Jun 2016, 06:33
Bunuel 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

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

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Re: A group of medical interns at Bohemus Medical School want to go on dat  [#permalink]

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02 Jun 2016, 12:18
Bunuel 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

5P5 = 120

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Re: A group of medical interns at Bohemus Medical School want to go on dat  [#permalink]

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07 Jun 2017, 07:41
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Bunuel 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)

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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Re: A group of medical interns at Bohemus Medical School want to go on dat  [#permalink]

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07 Jun 2017, 07:50
Bunuel 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 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).

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07 Jun 2017, 09:10
Because they are all straight, there are five pairs possible.

Total arrangements of these pairs:
5! = 120

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Re: A group of medical interns at Bohemus Medical School want to go on dat  [#permalink]

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09 Oct 2018, 11:52
Bunuel 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

$$?\,\,\,\,:\,\,\,\,\# \,\,\,{\text{guy - girl}}\,\,{\text{pairs}}$$

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.
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Re: A group of medical interns at Bohemus Medical School want to go on dat  [#permalink]

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12 Oct 2018, 08:00
Bunuel 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.

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Re: A group of medical interns at Bohemus Medical School want to go on dat   [#permalink] 12 Oct 2018, 08:00
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