How many ways can 6 people lined up to get on a bus?

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How many ways can 6 people lined up to get on a bus?

How many ways can 6 people lined up to get on a bus?
How many ways can 6 people lined up to get on a bus?

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How many ways can 6 people lined up to get on a bus?

University of Missouri - Columbia

There are

How many ways can 6 people lined up to get on a bus?
ways that 6 people can be lined up to get on the bus. (That is because there are 6 ways to choose who is first, for each of those choices, there are 5 ways to choose who is second, and so on).

There are

How many ways can 6 people lined up to get on a bus?
ways to line up 6 people placing together the 2 people who refuse to be next to each other.


{That is because there are ways to arrange the other 4 people,
ways to arrange the 2 people who refuse to be next to each other,
and places to insert the problem pair in the line formed by tho other 4).

Since

How many ways can 6 people lined up to get on a bus?
of the
How many ways can 6 people lined up to get on a bus?
ways that 6 people can be lined up to get on the bus place together the 2 people refuse to be next to each other,


there are ways to line up the 6 people keeping apart the 2 people who refuse to be next to each other.

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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!

(c) If 2 specific persons, among 6, refuse to follow each other, how many ways are possible ?

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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