A committee of five people is to be chosen from a club that boasts a membership
of 10 men and 12 women. How many ways can the committee be formed if it is
to contain at least two women? How many ways if, in addition, one particular
man and one particular woman who are members of the club refuse to serve
together on the committee?

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(12C2)*(20C3) for the first one

(12C2)*(20C3)-(2C2)*(11C1)(19C2) for the second question

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