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Math team problem
1.

15 people sit around the round table.

P( 15, 15)/ 15 = 14!

B sits next to a.

2*P( 14, 14)/ 14 = 13! *2

B sits on the right of a.

P( 14, 14)/ 14 = 13!

If b refuses to sit next to a

14! - 13! *2

= 13! * 12

=74724249600

If b just refuses to sit on the right side of a

14! - 13!

= 13! * 13

=8095 1270400

2.

(All combinations)-(It's a pity that all five people who can only play full-back are selected)-(It's a pity that all eight people who can only play full-back are selected)

=C( 1 1, 15) - C(6, 10) - C(3,7)

= 15! /(4! 1 1! ) + 10! /(6! 4! ) + 7! /(3! 4! )

= 16 10

3.

First, choose seats for five people who are always in the front row, then choose seats for four people who are always in the back row, and then choose seats for the rest.

P(5.8)* P(4.8)* P(5.7)

=(8! /3! )*(8! /4! )*(7! /2! )

=28449792000