How many ways can 5 persons line up to get on a bus?

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In how many ways can five people be seated in a row of five seats?

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(a) In how many ways can 6 people be lined up to get on a bus?
Answer = 6! (b) If 3 specific persons, among 6, insist on following each other, how many ways are possible?

Answer = 4! * 3!

Answer = 6! - 5! * 2

I can't figure out how we got the answer of part (c). May you explain how to think in order to solve such question

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6. in how many ways can five person's line up to ride a bus

Using the Simple Permutation Formula:

In how many ways can five people line up to get on a bus, but two of the people refuse to stand next to each other?
Suppose the 5 people are A,B,C,D, and E. Suppose C and D are the two that dont want to stand next to each other. If there were no restrictions on how the stand, and anybody could stand next to anybody else, the answer would be 5! or 120. However we must subtract from that number, the number of ways C could stand immediately IN FRONT OF D, and also subtract the number of ways C could stand immediately BEHIND D. We consider this as 3 single people A,B, and E plus 1 couple CD. This is 4 things, or 4!. We double that because there are also 4! ways in which we could have the four things A,B, and E plus the couple DC. So the answer is 5! - 2�4! = 120 - 2*24 = 120 - 48 = 72 ways. Edwin