A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet (he only drinks red wine), all from different wineries. a. If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? b. If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to do this? c. If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety?
A friend of mine is giving a dinner party. His current
wine supply includes 8 bottles of zinfandel, 10 of merlot,
and 12 of cabernet (he only drinks red wine), all from
different wineries.
a. If he wants to serve 3 bottles of zinfandel and serving
order is important, how many ways are there to do
this?
b. If 6 bottles of wine are to be randomly selected from
the 30 for serving, how many ways are there to do
this?
c. If 6 bottles are randomly selected, how many ways
are there to obtain two bottles of each variety?
d. If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety
being chosen?
e. If 6 bottles are randomly selected, what is the probability that all of them are the same variety?
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