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

b. how many ways are there to assign the 10 positions by selecting players from the 13 people who show up?

c. of the 13 people who show up, three are women. how many ways are there to choose 10 players to take the field if at least one of these players must be a woman?

Question

Mathematics

Dominic Greene

13 April, 17:14

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

b. how many ways are there to assign the 10 positions by selecting players from the 13 people who show up?

c. of the 13 people who show up, three are women. how many ways are there to choose 10 players to take the field if at least one of these players must be a woman?

+5

Answers (1)

Know the Answer?

Tiger · 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.