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
The number of ways to choose 1 member from the house of assembly is:
\(\binom{3}{1} = 3\)
The number of ways to choose 5 members from the state commissioners is:
\(\binom{9}{5}\) = 126
Thus, the total number of ways to form the committee is:
\(\text{Total ways} = \binom{3}{1} \times \binom{9}{5}\) = 3 \(\times\) 126 = 378
The total number of ways to form the committee, including one member from the house of assembly, is 378 Ways.
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