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?
Since Ozo is a boy and must be in the sub-committee, we have 2 spaces for the boys and 2 for the girls.
= \(^{4}C_{2} \times ^{3}C_{2} \)
= \(\frac{4!}{(4 - 2)! 2!} \times \frac{3!}{(3 - 2)! 2!} = 6 \times 3 = 18\)
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