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...

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?

Answer Details

The problem states that a sub-committee must be formed consisting of 3 boys and 2 girls. Also, Ozo must be on the sub-committee. This means that we already have one of the three boys chosen. We need to choose two more boys from the remaining four boys, and two girls from the three girls. The number of ways to choose two boys from the remaining four boys is given by the combination formula: C(4,2) = 6. (Alternatively, we can list all the possible combinations of two boys from the remaining four boys: Kofi and John, Kofi and Ojo, Kofi and James, John and Ojo, John and James, Ojo and James. This gives us a total of 6 combinations.) Similarly, the number of ways to choose two girls from the three girls is given by the combination formula: C(3,2) = 3. (Alternatively, we can list all the possible combinations of two girls from the three girls: Rose and Ugo, Rose and Ama, Ugo and Ama. This gives us a total of 3 combinations.) To find the total number of ways to choose the sub-committee, we multiply the number of ways to choose two boys and two girls: 6 x 3 = 18. Therefore, the answer is 18.