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The mathematics club has 9 students. Their coach needs to form a group to represent the school in a national competition. (a) How many groups

The mathematics club has 9 students. Their coach needs to form a group to represent the school in a national competition.

(a) How many groups of four can be chosen?

(b) If the club contains 5 boys and 4 girls, how many groups of four contain two boys and two girls?

(c) If the club contains 5 boys and 4 girls, how many groups of four contain at most three boys?

(d) If the club contains 5 boys and 4 girls, how many groups of four contain at least one woman?

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