A friend of mine is giving a dinner party. His current wineries. wine supply ind

Question

A friend of mine is giving a dinner party. His current wineries. wine supply indludes s bottles of zinfandel, 9 of merlot, and 10 of cabernet (he only drinks red wine), all from differ a) If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? 990 ways If o bottles of wine are to be randomly selected from the 27 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 If 6 bottles are randomly selected, what is the probability that all of therm are the same variety? (Round your answer to three decimal places)

Explanation / Answer

a)

There are 8 bottles of zinfandel,

Number of ways three bottles are chosen where order is importent is 8P3

8P3 = 8! / (8-3)! = 336

b)

6 bottles of wine are randomly selected from 27 bottles by 27C6 ways.

27C6 = 27! / [ (27-6)! * 6! ] = 296010

c)

Number of ways that 2 bottles of each variety can be chosen from randomly selected 6 bottles is

8C2 * 9C2 * 10C2   = 45360

d)

P(2 bottles of each variety chosen from 6 bottles)

=n(2 bottles of each variety chosen from 6 bottles) / n( 6 bottles are chosen from 27 bottles)

= 45360 / 27C6

= 45360 / 296010

=0.153

e)

p(All bottles are same veriety from 6 bottles)

= n(All bottles are same veriety from 6 bottles) / n( 6 bottles are chosen from 27 bottles)

= ( 8P6 + 9P6 + 10P6 ) / 27P6

= 231840 / 213127200

= 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.