NECO 2023 · Paper 2 · Q5

From 10 male and 8 female staff in a school, a committee of 5 men and 3 women is to be set up. In how many ways can this be done if:

  1. (a)

    any man and any woman may be included?

  2. (b)

    the principal (a male) must be on the committee?

Worked solution (try it first)

(a)

  1. Choose 5 men from 10 and 3 women from 8, and multiply:  10C5×8C3\,{}^{10}C_5 \times {}^8C_3.
  2. =252×56=14 112= 252 \times 56 = 14\,112 ways.

(b)

  1. Put the principal on.
  2. Choose the other 4 men from the remaining 9:  9C4=126\,{}^9C_4 = 126.
  3. The women as before:  8C3=56\,{}^8C_3 = 56.
  4. So 126×56=7056126 \times 56 = 7056 ways.

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