A friend of mine is giving a dinner party. His current
winesupply includes 8 bottles of zinfandel...1 answer below »

A friend of mine is giving a dinner party. His current
winesupply includes 8 bottles of zinfandel, 10 of merlot and 12
ofcabernet (he only drinks red wine), all from different wineries.

a.) if he wants to serve 3 bottles of zinfandel and servingorder
is important, how many ways are there to do this?

b.) If 6 bottles of wine are to be randomly selected from the
30for serving, how many ways are there to do this?

c.) IF 6 bottles are randomly selected, how many ways are
thereto obtain two bottles of each variety?

d.) IF 6 bottles are randomly selected, what is the
probabilitythat this results in two bottles of each variety being
chosen?

e.) If 6 bottles are randomly selected, what is the
probabilitythat all of them are the same variety?

Jan 13 2021 04:44 PM

1 Approved Answer

k n
answered on
January 15, 2021

5
Ratings,(10 Votes)

Given, number of zinfandel bottles, z=8
Given, number of merlot bottles, m=10
Given, number of cabernet bottles, c=12

(a) Here, we have to make arrangements of 3 zinfandel bottles out of 8 zinfandel bottles

## 1 Approved Answer

January 15, 2021Given, number of zinfandel bottles, z=8

Given, number of merlot bottles, m=10

Given, number of cabernet bottles, c=12

(a)

Here, we have to make arrangements of 3 zinfandel bottles out of 8 zinfandel bottles

n=8;r=3

nPr=n!(n−r)!

8P3=8!(8−3)!=8!5!=8×7×6×5!5!=8×7×6=336

Therefore, 8P3=336

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