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

Question

In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women? (A) 45 (B) 350 (C) 4200 (D) 230

Tardigrade Admin · Accepted Answer

Out of 7 men, 3 men can be chosen in 7C3 ways and out of 5 women, 2 women can be chosen in 5C2 ways. Hence, the committee can be chosen in 7C3 × 5C2 = 350 ways.

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

$45$

$350$

$4200$

$230$

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.

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

45

350

4200

230