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In how many ways can 4 boys and 4 girls be arranged in a row

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In how many ways can 4 boys and 4 girls be arranged in a row [#permalink] New post 14 May 2019, 00:37
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Question Stats:

55% (01:32) correct 44% (01:36) wrong based on 9 sessions
In how many ways can 4 boys and 4 girls be arranged in a row such that no two boys and no two girls are next to each other?

(A) 1032

(B) 1152

(C) 1254

(D) 1432

(E) 1564
[Reveal] Spoiler: OA

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Re: In how many ways can 4 boys and 4 girls be arranged in a row [#permalink] New post 22 Aug 2019, 19:03
Carcass wrote:
In how many ways can 4 boys and 4 girls be arranged in a row such that no two boys and no two girls are next to each other?

(A) 1032

(B) 1152

(C) 1254

(D) 1432

(E) 1564


I think I'm finally getting alright at these!

seat 1 we can sit one of 4 boys. so 4 options.
seat 2 we can sit one 4 girls so 4 options.
seat 3 we can sit one of 3 REMAININg boys, so 3 options.
.... (continue the pattern)
and then we flip it the other way. so we multiply it by 2.

2*4!4! = 2 * 4^2 * *3^2 * 2^2 = 2 * 64 * 9 = 2 * 576 = 1152

(REPEAT)
Re: In how many ways can 4 boys and 4 girls be arranged in a row   [#permalink] 22 Aug 2019, 19:03
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In how many ways can 4 boys and 4 girls be arranged in a row

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