SOLUTION: A commitee of 9 is to be selected from 6 women and 8 men.in how many ways can this be done if the committee must contain at least 4 women?

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Question 604615: A commitee of 9 is to be selected from 6 women and 8 men.in how many ways can this be done if the committee must contain at least 4 women?
Answer by scott8148(6628) About Me  (Show Source):
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there are 6C4 ways of selecting 4 women from 6

there are 8C5 ways of selecting 5 men from 8

so there are (6C4 * 8C5) ways of selecting a 4 woman committee

there are 6C5 ways of selecting 5 women from 6

there are 8C4 ways of selecting 4 men from 8

so there are (6C5 * 8C4) ways of selecting a 5 woman committee

there is one way of selecting 6 women from 6

there are 8C3 ways of selecting 3 men from 8

so there are 8C3 ways of selecting a 6 woman committee

sum the three committee types for the answer