Harry, Peter and 7 girls sit in a row. Harry can't sit in an end seat. In how many ways can they be arranged?

2 answers:

4 0

All possibilities = 9!
possibilities that harry sits at an end = 8! + 8!
possibilities that harry doesn't sit at an end = 9! - 8! -8!

vekshin12 years ago

4 0

List of all possibilities, without restrictions (ie Harry can sit in any of the 9 seats): $9!$
List of all possibilities where Harry sits on either end: $2 \cdot 8!$

Hence, list of all possibilities where Harry doesn't sit on either end: $9! - 2 \cdot 8! = 282,240$ ways.

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