8th ed., §2.3, Exercise 30.a A friend of mine is giving a dinner party. His curr

Question

8th ed., §2.3, Exercise 30.a 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, all from different wineries.

A). If he wants to serve three 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 of wine are randomly selected, how many ways are there to obtain two bottles of each variety?

D). If 6 bottles of wine are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (Give your answer to the nearest thousandth.)

E). If 6 bottles of wine are randomly selected, what is the probability that all of them are the same variety?

Explanation / Answer

A)

8P3=8!/(8-3)!=8*7*6=336 ways.

B)

30C6=30!/6!24!=593775

C)

8C2*10C2*12C2=83160

D)

8C2*10C2*12C2/30C6=0.140053

E)

8C6+10C6+12C6/30C6=0.00195697

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