Henry is throwing a party for the end of the semester. He buys 30 unique bottles

Question

Henry is throwing a party for the end of the semester. He buys 30 unique bottles of wine (say, from 30 different wine producers). Of those 30 bottles, 10 are red wine, 14 are white wine, and 6 are rose.

(a) Henry serves 6 bottles (out of the 30) with dinner. Assuming that order is important, how many ways are there to do this?

(b) Again, Henry serves 6 bottles (out of the 30) with dinner, but now he requires that at least one red wine is served. Again assuming that order is important, how many ways are there to do this?

(c) If he selects 6 bottles at random, what is the probability that he selects 2 of each type? (Where the types are red, white, and rose.)

(d) If he selects 6 bottles at random, what is the probability that the bottles are all of the same type? (Where the types are red, white, and rose.)

Explanation / Answer

a) Total no of ways of select 6 bottles = 30C6 = 593775

b) At least one red wine = 30C6-20C6 = 555015

c) probability that he selects 2 of each type = (10C2*14C2*6C2)/(30C2) = 0.1034

d) Probability that the bottles are all of the same type = (10C6+14C6+6C6)/(30C6) = 0.0054

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