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 members of the committee be chosen so as to include one member of the house of assembly

  • A 378 ways
  • B 462 ways
  • C 840 ways
  • D 924 ways
jamb 2004mathematics

The correct answer is A. 378 ways

Since one member of the house of assembly must be included in the committee, we can first choose one member from the three members of the house of assembly in \(\binom{3}{1}\) ways.

The remaining five members of the committee can then be chosen from the nine state commissioners in \(\binom{9}{5}\) ways. Therefore, the total number of ways to form the committee is \(\binom{3}{1} \times \binom{9}{5} = 3 \times 126 = 378\) ways.

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