Question

Number of ways in which 7 seats around a table can be occupied by 15 persons

Answer 1

=15 P 7
=15! /( 15 -7)!
=15! / 8!
=8! *9*10 *11 * 12 *13 *14*15 /8!
=32432400

Answer 2

$15 \: fac \div (15 - 7) \: fac \\ = 15fac \div 8fac \\ = 15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \\ = 32432400$


Since we have to choose and 7 people out of the given 15 people and the order does matter as the arrangement of different people in different chairs will give different results.