A committee consists of 5 boys namely: Kofi, John, Ojo, Ozo and James and 3 girls namely: Rose, Ugo and Ama. In how many ways can a sub-committee consisting of 3 boys and 2 girls be chosen, if Ozo must be on the sub-committee?
-
A.
35 -
B.
30 -
C.
18 -
D.
12
Correct Answer: Option C
Explanation
Since Ozo is a boy and must be in the sub-committee, we have 2 spaces for the boys and 2 for the girls.
= (^{4}C_{2} times ^{3}C_{2} )
= (frac{4!}{(4 – 2)! 2!} times frac{3!}{(3 – 2)! 2!} = 6 times 3 = 18)