Question

Thirteen people on a softball team show up for a game.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?

Answer 1

Total number of people = 13

A:

Number of ways to choose 10 players to take the field = 13C10

=
`(13!)/(10!3!)`

= 286

B:

This is given as: 13P10

=
`(13!)/((13-10)!)` =
`(13!)/(3!)`

= 1037836800

C:

This is given as:

(3C1 x 10C9) + (3C2 x 10C8) + (3C3 x 10C7)

Solving this we get the answer as = 285