A friend of mine is giving a dinner party. His current wine supply includes 8 bo

Question

A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 12 of merlot, and 10 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? 168 times ways (b)If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to do this? ways (c)If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (Round your answer to three decimal places.) (e) If 6 bottles are randomly selected, what is the probability that all of them are the same variety? (Round your answer to three decimal places.)

Explanation / Answer

a)

8C3 = 56

b)

30C6= 593775

c)

8C2 * 12C2 * 10C2 = 83160

d)

we have 593775 ways to do without restrictions and 83160 with the restriction so

P = 83160 / 593775 = 0.14

e)

I can gladly help you burt you should post it in a new question

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