Finite Math
posted by Sam on .
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 nonfish
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?

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 nofish, which would be C(9,6) or 84
so no of cases with at least 1 fish dinner is 1237684 = 12292