A friend of mine is giving a dinner party. His current wine supply includes 10 b

Question

A friend of mine is giving a dinner party. His current wine supply includes 10 bottles of zinfandel, 12 of merlot, and 9 of cabernet (he only drinks red wine), all from different wineries.

a) If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety?

b)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.)

c) 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

10 Z , 12 M and 9 C

a) to get 2 bottles of each , 10C2*12C2*9C2 =45*66*36=106920

b) P( 2 bottles of each )=106920 / 31C6 (because there are 10+12+9=31 total bottles to choose from ) =106920 / 736281=0.1452

c) P(all same)= (10C6+12C6+9C6)/31C6 (because one can choose all Z or all M or all C)

=147/736281

=0.000199652

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.