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

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A pod of 6 dolphins always swims single file, with 3 females  [#permalink]

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New post Updated on: 24 Aug 2014, 05:53
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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
Spoiler: OA

Originally posted by sahil7389 on 24 Aug 2014, 03:17.
Last edited by Bunuel on 24 Aug 2014, 05:53, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A pod of 6 dolphins always swims single file, with 3 females  [#permalink]

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New post 24 Aug 2014, 05:58
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1
sahil7389 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


3 females at the front can be arranged in 3! ways;
3 males at the rear can also be arranged in 3! ways.

To get the total number of arrangements multiply: total = 3!*3! = 36.

Answer: B.
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Re: A pod of 6 dolphins always swims single file, with 3 females  [#permalink]

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New post 22 Sep 2016, 05:08
Bunuel wrote:
sahil7389 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


3 females at the front can be arranged in 3! ways;
3 males at the rear can also be arranged in 3! ways.

To get the total number of arrangements multiply: total = 3!*3! = 36.

Answer: B.


Why isn't the 3! x 3! divided by 3! x 3!, given that the dolphins Male and Female are 'repeated'?
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Re: A pod of 6 dolphins always swims single file, with 3 females  [#permalink]

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New post 12 Nov 2016, 06:32
sahil7389 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


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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Re: A pod of 6 dolphins always swims single file, with 3 females  [#permalink]

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New post 20 Nov 2017, 04:32
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Re: A pod of 6 dolphins always swims single file, with 3 females &nbs [#permalink] 20 Nov 2017, 04:32
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