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Combinations: Selecting members of committee

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A club has 28 members, and 6 members must be selected to make a committee.
a) Of the 28 members, 15 are men and the rest are women. How many ways can the 6 member committee can be selected if there are to be 4 men and 2 women on the committee?
b) How many different ways can the committee be selected if one person must be the chairman and another person must be a secretary/treasurer. ( the other 4 persons on the committee do not hold any titles).
c) How many different ways can the committee be selected if 3 members are to be automatically included in the committee?
d) How many different ways can the committee be selected if 4 of the members can't be on the committee?

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The expert examines selecting members of committees.

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Please understand the difference between permutations and combinations first. While the former denotes the order of arranging things, the latter only denotes the ...

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