Please help, committee creation math problem?

A group of 9 people, 5 woman, and 4 men needs to select a committee of 3 from Among its members to attend a state conference.

A) determine how many possible different 3 person committees could be created

B)Assuming that the selection are made randomly, determine how many of the possible committees would contain :

Women Men

1). 0 3

2). 1 2

3). 2 1

4). 3 0

Thank you very much!

2 Answers

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  • 7 years ago
    Best Answer

    A committee has no structure, nor ordering, so we use combinations, not permutations to calculate them. If we choose a committee of r members from a group of n members, we can from nCr different committees, where nCr = n!/(r!(n-r)!).

    A 9C3 = 9!/3!6! = 9*8*7/6 = 84

    B In B we have to multiply the ways of choosing women times the ways of choosing men. In the first, there is 1 way to choose 0 from any number. There is 4C3 ways of choosing 3 men from 4. (i.e. 4 altogether, one for each different unchosen man. 1*4 = 4

    5*6 = 30

    10*4 = 40

    10*1 = 10

  • riobe
    Lv 4
    3 years ago

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