Question

A) how many ways are there to choose 10 players to take the field?

Answer 1

A. C(13, 10) = 13! = 13·12·11 = 13 · 2 · 11 = 286.C(13, 10) = 13! = 13·12·11 = 13 · 2 · 11 = 286.

B. P(13,10)= 13! =13! =13·12·11·10·9·8·7·6·5·4. (13−10)! 3!

C. f there is exactly one woman chosen, this is possible in C(10, 9)C(3, 1) =

10! 3!

9!1! 1!2! 10! 3!

8!2! 2!1! 10! 3!

7!3! 3!0!

= 10 · 3 = 30 ways; two women chosen — in C(10,8)C(3,2) =

= 45·3 = 135 ways; three women chosen — in C(10, 7)C(3, 3) =

= 10·9·8 ·1 = 120 ways. Altogether there are 30+135+120 = 285 1·2·3

possible choices.