1.

In how many ways can a committee of three be chosen from four married couples if all are equally eligible

Answer»

There are 8 persons (4 men and 4 women). A committee is to be formed consisting of 3 persons so that 1 particular man has to be in the committee. Excluding that particular man there are 7 persons ( 3 men and 4 women) from which 2 are to be chosen. And the choices are (i) 2 men and no woman (ii) 1 man and 1 woman and (iii) 2 women and no man. This leads to 3Cx 4C+3Cx 4C+ 3Cx 4C

=3 x 1+3 x 4+1 x  6

=21



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