Question

WebAssige merlst, and of cabernet he ory drinks red from ifferent wineniss (aj if he wants to serve 3 oittlies of sdandet and srng sder s mpotend, how many ways are there to do this lbj Ir 6 botles of wine are to be randonmly selted there to do te? for serving, how many ways are the (e) It 6 bottles are randomly selected, how many ways ae thee t oties of each variety? (d) If 6 botties are randomty selected, wat is the prodstady thet thiseut in tny beitles of each variety being chosent (hound ar to three deeimel ces (e) If 6 botties are randomly selected, whet is the pesabilty tet w o them are the same variety? (Round your answer to three decimal plaes Need Help?

Answer 1

There is 9 bottles of zinfandel,10 of merlot,8 of cabernet.

a) If he wants to serve 3 bottles of zinfandel it can be done in ⁹P₃ ( since serving order is important we use permutations)ways=504

b) If 6 serving are to be chosen from 27 it can be done in ²⁷C₆ ways=296010

c) If 6 are chosen ways to choose 2 of each variety= ⁹C₂* ¹⁰C₂*⁸C₂ =45360

d) Probablility of choosing 2 from each variety = (⁹C₂* ¹⁰C₂*⁸C₂ )/²⁷C_{6= 0.1532}

e) If 6 are chosen probability of choosing all from same= (⁹C₆+¹⁰C₆+⁸C₆)/²⁷C_6=0.001087