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A resort manager is choosing a committee of four people to discuss employment issues. They' II choose from eight housekeepers, three desk clerks, and five mai ntenance w orkers. H ow many possible comma ttees are there if there have to be at least two housekeeper
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A resort manager is choosing a committee of four people to discuss employment issues. They' II choose from eight housekeepers, three desk clerks, and five mai ntenance w orkers. H ow many possible comma ttees are there if there have to be at least two housekeeper $\newline$ (Ctrl)

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Counting principle

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Q. A resort manager is choosing a committee of four people to discuss employment issues. They' II choose from eight housekeepers, three desk clerks, and five mai ntenance w orkers. H ow many possible comma ttees are there if there have to be at least two housekeeper

\newline

(Ctrl)

Calculate total ways: Calculate the total number of ways to choose two housekeepers from eight. $\newline$ Using the combination formula: $C(n, k) = \frac{n!}{k!(n-k)!}$ $\newline$ $C(8, 2) = \frac{8!}{[2!(8-2)!]} = 28$
Choose remaining members: Calculate the number of ways to choose the remaining two members from the remaining staff ( $3$ desk clerks + $5$ maintenance workers = $8$ staff). $\newline$ $C(8, 2) = \frac{8!}{2!(8-2)!} = 28$
Calculate total committees: Calculate the total number of possible committees by multiplying the combinations. $\newline$ Total committees = $28$ (housekeepers) $\times$ $28$ (other staff) = $784$

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