Posted by **Sam** on Wednesday, October 22, 2008 at 12:54am.

A travel writer is on a cruise. After the cruise, he is going to write

a magazine article evaluating the quality of the cruise, including

the food. (For instance, "On the first night, I had the shark steak

Florentine ... which was superb.") The dinner menu, which

is the same every evening, has 8 fish entrees and 9 non-fish

entrees (e.g., beef, pork, etc.). Each night the writer

selects a different entree and records the selection in his

notebook. The cruise will last 6 nights, so there will be 6 dinnner

entrees recorded.

How many overall outcomes are possible?

In how many possible overall outcomes would fish entrees appear

exactly 4 times?

In how many possible overall outcomes would fish entrees appear at most

4 times?

In how many possible overall outcomes would fish entrees appear at least

1 time?

- Finite Math -
**Reiny**, Wednesday, October 22, 2008 at 8:49am
How many overall outcomes are possible? -- C(17,6) = 12376

In how many possible overall outcomes would fish entrees appear exactly 4 times?

C(8,4)xC(9,2) = 2520

In how many possible overall outcomes would fish entrees appear at least 1 time?

we must exclude the no of cases of no-fish, which would be C(9,6) or 84

so no of cases with at least 1 fish dinner is 12376-84 = 12292

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