Question 1039768: Committees of men and women. We want to select a committee of five members from a group of five women and six men. The order of selection is irrelevant.
How many committees can we make with fewer men than women? Suggestion: There could be three women and two men, four women and one man, or five women.
(Fill in the blank below and give your answer as a whole number.)
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
three women and two men, or
four women and one man, or
five women and no men
(5 women choose 3) and (6 men choose 2) or
(5 women choose 4) and (6 men choose 1) or
(5 women choose 5) and (6 men choose 0) =
"And" means multiply, "or" means add.
(5C3)×(6C2) + (5C4)×(6C1) + (5C5)×(6C0)
[There is always 1 way to choose 0, and that 1 way is
'to not choose any'.]
Edwin
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