Question

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

Answer:

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Step-by-step explanation:

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Answer 2

Twenty people on a softball team show up for a game and of them, six are women. It is aim ed to assign the 10 positions of the softball team from those who have shown up.

• The number of ways to choose 10 players such that at least two of these players  must be a woman is 179465. The solution can be achieved by (20C10) - (14C10 + 13C9 * 6C1) = 179465
• The number of ways are there to choose 10 players such that at most four players must be  women are 171743.
• This can be explained as: (14C6 * 6C4) + (14C7 * 6C3) + (14C8 * 6C2) + (14C9 * 6C1) + (14C10) = 45045 + 68640 + 45045 + 12012 + 1001 = 171743