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 Question from raymond, a student: In how many ways can 4 boys and 4 girls be seated in a row if they may sit anywhere

Hi Raymond,

If anyone can sit anywhere you could just ask,

In how many ways can 8 people be seated in a row?

I'm going to illustrate with 3 people to save me some typing.

In how many ways can 3 people be seated in a row?

I have three people Mary, Bob and Susan and three chairs in a row. I am going to start by placing someone i the first chair. I have three choices so after seating the first person the arrangement is one of the three possibilities

M
B
S

Regardless of who I seat first I now have two choices for the second seat. The possibilities are

M B
M S
B M
B S
S M
S B

Hence at this stage there are 3 × 2 = 6 possible seating arrangements. For each of these there is just one choice for the final seat so the possible arrangements are

M B  S
M S B
B M S
B S M
S M B
S B M

The number of possible arrangements is then 3 × 2 × 1 = 6.

Now try your problem with 8 people.

Penny

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