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In how many ways can a committee of 2 women and 3 men be chosen…

In how many ways can a committee of 2 women and 3 men be chosen from 6 men and 5 women?
  • A.
    100
  • B.
    200
  • C.
    30
  • D.
    50
Correct Answer: Option B
Explanation

A committee of 2 women and 3 men can be chosen from 6 men and 5 women, in (^{5}C_{2}) x (^{6}C_{3}) ways
= (frac{5!}{(5 – 2)!2!} times {frac{6!}{(6 – 3)!3!}})
= (frac{5!}{3!2!} times {frac{6!}{3 times 3!}})
= (frac{5 times 4 times 3!}{3! times 2!} times {frac{6 times 5 times 4 times 3!}{3! times 3!}})
= (frac{5 times 4}{1 times 2} times {frac{6 times 5 times 4}{1 times 2 times 3}})
= 10 x (frac{6 times 20}{6})
= 200