A friend of mine is giving a dinner party. His current wine supply includes 9 bo

Question

A friend of mine is giving a dinner party. His current wine supply includes 9 bottles of zinfandel, 10 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries

A friend of mine is giving a dinner party. His current wine supply includes 9 bottles of zinfandel, 10 of merlot, and 11 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? X 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)

Number of ways that 3 zinfandel bottle serve when order is importent = 9 *8 * 7 =504

b)

6 bottles can be chosen from 30 bottles by 30C6 ways.

30C6 = 30! / ( (30-6)! * 6!) = 593775

c)

Number of ways that two bottles are each veriety are 9C2 * 10C2 * 11C2 = 89100

d)

Probability that two bottles of each veriety chosen = Number of ways that two bottles are each veriety chosen/

total number of ways that 6 bottles are chosen from 30

= 9C2 * 10C2 * 11C2 / 30C6

= 0.150

e)

Probability that all of them are same veriety = (9C6 + 10C6 + 11C6) / 30C6

= 0.001

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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