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. $230$

Answer 1

Answer: (B)

$350$

Answer 2

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.