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A pod of 6 dolphins always swims single file, with 3 females

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by BTGmoderatorDC » Mon Jun 10, 2019 8:47 pm

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A pod of 6 dolphins always swims single file, with 3 females at the front and 3 males in the rear. In how many different arrangements can the dolphins swim?

A. 20
B. 36
C. 40
D. 18
E. 54

OA B

Source: Manhattan Prep
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by Jay@ManhattanReview » Mon Jun 10, 2019 9:03 pm
BTGmoderatorDC wrote:A pod of 6 dolphins always swims single file, with 3 females at the front and 3 males in the rear. In how many different arrangements can the dolphins swim?

A. 20
B. 36
C. 40
D. 18
E. 54

OA B

Source: Manhattan Prep
With the given constraint, the 3 females can arrange themselves in 3! = 6 ways; similarly, the 3 males can arrange themselves in 3! = 6 ways. Thus, the total number of ways = 6*6 = 36.

The correct answer: B

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Fri Jun 14, 2019 2:41 pm
BTGmoderatorDC wrote:A pod of 6 dolphins always swims single file, with 3 females at the front and 3 males in the rear. In how many different arrangements can the dolphins swim?

A. 20
B. 36
C. 40
D. 18
E. 54

OA B

Source: Manhattan Prep
We are given that a pod of 6 dolphins always swims single file, with 3 females at the front and 3 males in the rear. Thus:

The number of ways to arrange the 3 female dolphins in the front is 3! = 3 x 2 x 1 = 6.

The number of ways to arrange the 3 male dolphins is in the rear is 3! = 3 x 2 x 1 = 6.

Thus, the number of ways to arrange all the dolphins is 6 x 6 = 36 ways.

Answer: B

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