Question

2. Twenty people on a softball team show up for a game and of them, six are women. We aim to assign the 10 positions of the softball team from those who have shown up. (a) How many ways are there to choose 10 players such that at least two of these players must be a woman? (b) How many ways are there to choose 10 players such that at most four players must be women? (c) How many ways are to choose 10 players such none of these players are women?

Answer 1

(a). The number of ways to choose 10 players such that at least two of these players must be women = 171743

(b). The number of ways to choose 10 players such that at most four players must be women

= 171743

(c). The number of ways to choose 10 players such that no women player is selected in the team

= 1001