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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]  14 May 2019, 00:38
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Question Stats:

85% (00:52) correct 14% (00:00) wrong based on 21 sessions
In how many ways can 4 boys and 4 girls be arranged in a row such that boys and girls alternate their positions (that is, boy girl)?

(A) 1032

(B) 1152

(C) 1254

(D) 1432

(E) 1564
[Reveal] Spoiler: OA

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Manager
Joined: 22 Aug 2019
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Re: In how many ways can 4 boys and 4 girls be arranged in a row [#permalink]  22 Aug 2019, 19:00
Carcass wrote:
In how many ways can 4 boys and 4 girls be arranged in a row such that boys and girls alternate their positions (that is, boy girl)?

(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
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Re: In how many ways can 4 boys and 4 girls be arranged in a row [#permalink]  29 Nov 2019, 02:53
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Re: In how many ways can 4 boys and 4 girls be arranged in a row [#permalink]  03 Dec 2019, 11:58
Found two well exlpained answers at GMATCLUB.

1st:
First arrange the 4 boys in 4! in a way such B_B_B_B ---> 4!
Then, girls can be arranged in two different ways, G first or B first. So, GBGBGBGB, so girls also in 4!, Or BGBGBGBG.. 4! --> 2*4!
Answer = 4!(4!+4!)=4!*2*4!=24*24*2=576*2=1152

B

2nd:
how many arrangements are there of 4 girls=4!=24, AND of 4 boys=4!=24, AND multiply by two since we could begin seating girls or boys first, so total arrangements is 24*24*2=1152
Re: In how many ways can 4 boys and 4 girls be arranged in a row   [#permalink] 03 Dec 2019, 11:58
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# In how many ways can 4 boys and 4 girls be arranged in a row

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