Respuesta :
The number of ways there to pick five people for a committee is if there are six men and eight women, and the selection must include at least one man and one woman 1940.
What is the combination?
Combinations are mathematical operations that count the number of possible configurations for a set of items where the order of the selection is irrelevant. In combinations, you can select the items in any order.
There are 6 different men and 8 different women.
The committee must include at least 1 man and 1 woman.
Thus let us first see the possible cases where this condition does not satisfy.
We select 5 men and no women = (6C5)(8C0) = (6)(1) =6
We select 5 women and no men = (8C5)(6C0) = 56
Total no.of possibilities of selecting 5 people in any way = 14C5 = 2002
So the no.of possibilities with at least 1 man and 1 woman = 2002 - 6 - 56 = 1940.
Hence, the number of ways there to pick five people for a committee is if there are six men and eight women, and the selection must include at least one man and one woman 1940.
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