SOLUTION: In how many ways can Al, Bob, Carol, Don, Ed, Faye, and George be seated in a row of seven seats so that Al, Bob, and Carol occupy consecutive seats in some order?

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Question 1157461: In how many ways can Al, Bob, Carol, Don, Ed, Faye, and George be seated in a row of seven seats so that Al, Bob, and Carol occupy consecutive seats in some order?
Answer by greenestamps(13200) About Me  (Show Source):
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(1) Put Al, Bob, and Carol together in a group. Within that group there are 3!=6 ways to arrange the three of them.

(2) Treating those 3 as a group, we now have 5 things to arrange in a line. The number of ways to do that is 5!=120.

The total number of ways to arrange the seven people with Al, Bob, and Carol in consecutive seats is 6*120 = 720.