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Six children, three boys, and three girls

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Six children, three boys, and three girls [#permalink] New post 19 Jul 2018, 05:55
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Question Stats:

71% (01:13) correct 28% (01:09) wrong based on 21 sessions
Six children, three boys, and three girls sit in a row on a park bench. How many arrangements of children are possible if no boy can sit on either end of the bench?

Indicate all possible values.

A. 46,656

B. 38,880

C. 1,256

D. 144

E. 38
[Reveal] Spoiler: OA

Last edited by Carcass on 15 Oct 2019, 03:39, edited 4 times in total.
Edited by Carcass
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Re: Counting [#permalink] New post 19 Jul 2018, 18:01
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imransuet wrote:
Please provide solution with details



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Re: Six children, three boys, and three girls [#permalink] New post 30 Sep 2019, 03:21
this question is actual quite hard
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Re: Six children, three boys, and three girls [#permalink] New post 12 Oct 2019, 11:13
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We have 2 girls sit at the 2 ends, therefore we have P(3,2) = 6 (order is important here so we can't use C). That will leave 4 people, 3 boys and 1 girl in the middle. Since they can sit anywhere, in whatever arrangment, we have P(4,4) or 4! = 24. Total possible arrangement is 6*24 = 144. Answer is D.
Re: Six children, three boys, and three girls   [#permalink] 12 Oct 2019, 11:13
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Six children, three boys, and three girls

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