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  4. In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?

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Q. In how many ways a committee consisting of $3$ men and $2$ women, can be chosen from $7$ men and $5$ women?

Permutations and Combinations

Solution:

Out of $7$ men, $3$ men can be chosen in $^{7}C_{3}$ ways and out of $5$ women, $2$ women can be chosen in $^{5}C_{2}$ ways. Hence, the committee can be chosen in $^{7}C_{3} \times\,{}^{5}C_{2} = 350$ ways.