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In how many ways can you sit 8 people on a bench if 3 of them must sit together? a) 720 b) 2,160 c) 2,400 d) 4,320 e) 40,320

i'm getting 'e' but that is not OA

Say 8 people are {A, B, C, D, E, F, G, H} and A, B and C must sit together. Consider them as one unit {ABC}, so we'll have total of 6 units: {ABC}, {D}, {E}, {F}, {G}, {H}, which can be arranged in 6! ways. Now, A, B and C within their unit can be arranged in 3! ways, which gives total of 6!*3!=4,320 different arrangements.

Re: In how many ways can you sit 8 people on a bench if 3 of [#permalink]
12 Mar 2012, 09:30

1

This post received KUDOS

Expert's post

Gavan wrote:

thanks!

did you consider following arrangements? 1: -{D},{ABC}, {E}, {F}, {G}, {H}, 2: -{D},{E}, {F},{ABC}, {G}, {H}, 3: - ..

Please clarify.

6 distinct object can be arranged in 6! different ways, so 6 units {ABC}, {D}, {E}, {F}, {G}, {H} can be arranged in 6! different ways, which takes cares of all possible cases.

Re: In how many ways can you sit 8 people on a bench if 3 of [#permalink]
23 Feb 2014, 17:16

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