Question

Please help!!
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?

Answer 1

The number of ways that all nine people can sit in the row anywhere is 9*8*7*6*5*4*3*2*1 = 362,880.
WITH Harry in an end seat, there are 1 * 8*7*6*5*4*3*2*1 plus 1*2*3*4*5*6*7*8*1 ways, 80,640, the nine people to sit with Harry at one end of the row or the other end.
The number of ways all 9 people can arrange themselves on the row MINUS the number of ways the 9 people can arrange themselves on the row with Harry in the left end seat or the right end seat = the number of ways the nine people can arrange themselves on the row with Harry being someplace other than the end of the row.
362,880 - 80,640 = 282, 240 ways with Harry not sitting at the end of the row.