In how many ways can you sit 8 people on a bench if 3 of them must sit together?  Choose the correct choice from the following.
A) 720 B) 2,160 C) 2,400 D) 4,320 E) 40,320
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.   Answer: 4,320.
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In how many ways can you sit 8 people on a bench if 3 of them must sit together?