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“A resort manager is choosing a committee of four people to discuss employment issues. He’ll choose...

“A resort manager is choosing a committee of four people to discuss employment issues. He’ll choose from eight housekeepers, three desk clerks, and five maintenance workers. How many possible committees are there if there have to be at least two housekeepers?”

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Answer #1

Total are 8 + 3 + 5 = 16 workers

We need at least two housekeepers.

So, total ways = C(8, 2) * C(8, 2) + C(8, 3) * C(8, 1) + C(8, 4)*C(8, 0)

First C(8, 2) showing ways for 2 housekeepers, and next C(8, 2) showing rest 2 members from other workers and so on.

Total way = 28*28 + 56*8 + 70*1

= 1302

Hence, there are total 1302 ways.

Please comment if any doubt. Thank you.

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