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