JAMB 2004 · UME · Q47

A committee of six is to be formed by a state governor from nine state commissioners and three members of the state house of assembly. In how many ways can the committee be chosen so as to include one member of the house of assembly?

Worked solution (try it first)
  1. Choose the one assembly member from three: 3C1=3^3C_1 = 3 ways.
  2. The other 5 places go to commissioners, 5 from 9: 9C5=126^9C_5 = 126 ways.
  3. Multiply: 3×126=3783 \times 126 = 378 ways, option D.

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