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A committee of six people is chosen from five senators and eleven representatives. How many committees are possiblethere are to be three senators and three representatives on the Committee

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SOLUTION

This means we are to select 3 persons from 5 senators and 3 persons from 11 representatives. This can be done by

[tex]^5C_3\times^{11}C_3\text{ ways }[/tex]

So we have

[tex]\begin{gathered} ^5C_3\times^{11}C_3\text{ ways } \\ 10\times165 \\ =1650\text{ ways } \end{gathered}[/tex]

Hence the answer is 1650 ways

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