Question

8). A school dance committee is to consist of 2 freshman, 3 sophomores, 4 juniors, and...

8). A school dance committee is to consist of 2 freshman, 3 sophomores, 4 juniors, and 5 seniors. If 7 freshman, 7 sophomores, 7 juniors, and 9 seniors are eligible to be on the committee, in how many ways can the committee be chosen?

7). 13 players for 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 form the 13 people who show up?

c. Of the 13 people who show up, 3 are women. How many ways are there to choose 10 players to take the field if at least one of these players must be women?

10). From a group of 6 men and 8 women a committee consisting of 4 men and 3 women is to be formed. How many different committees are possible if:

a. 2 of the men refuse to serve together?

b. 2 of the women refuse to serve together?

c. 1 man and 1 woman refuse to serve together?

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