The Department of Applied Mathematics and Statistics (AMS) of a state university has 24 full-time faculty members, of whom 4 are women and 20 are men. A committee of 3 faculty members is to be selected from this group in order to study the issue of purchasing a new copier. a. How many ways are there to select a committee? b. How many ways are there to select a committee that has more women than men? c. If the positions in the committee are titled chair, vice chair, and secretary, in how many ways can this committee be formed among the 24 AMS faculty members?

Question

Mathematics

Stacy

15 September, 23:30

The Department of Applied Mathematics and Statistics (AMS) of a state university has 24 full-time faculty members, of whom 4 are women and 20 are men. A committee of 3 faculty members is to be selected from this group in order to study the issue of purchasing a new copier. a. How many ways are there to select a committee? b. How many ways are there to select a committee that has more women than men? c. If the positions in the committee are titled chair, vice chair, and secretary, in how many ways can this committee be formed among the 24 AMS faculty members?

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Answers (1)

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Rory Bowman · Answer 1

a) (24 comb 3) = C (24,3) = 2024

b) ((4 comb 2) x (20 comb 1)) = C (4,2) x C (20,1) = 6 x 20 = 120

c) (24 x 23 x 22) = 12144

Step-by-step explanation:

a) Since no restriction or order is stated.

b) Since this is the only arrangement in the committee that can have more women than men. 2 women and 1 man.

c) Since we are taking positions in the committee titled chair, vice chair, and secretary. It means others can come in any arrangement.