Probability help please:

Question

Assume that there are 8 different issues of Newsweek, 7 different issues of Popular Science, and 3 different issues of Time, including the December 1st issue, on the rack. You choose 4 of them at random.
(1) What is the probability that exactly 2 are issues issue of Newsweek?


(2) What is the probability that you choose the December 1st issue of Time?

Answer 1

First of all, let's assume all the magazines are distinct.

 

There are 8+7+3 = 18 magazines on the rack in total.

 

Then the total number of ways to choose 4 is

 

C(18,4) = 18·17·16·15 / 4! = 3060

 

 

Part 1:

 

There are C(8,2) = 8·7 / 2! = 28 ways to choose the two Newsweeks.

 

There are C(10,2) = 10·9 / 2! = 45 ways to choose two that are not Newsweek.

 

Thus the probability of getting two Newsweek among the four drawn is

 

28·45 / 3060 = 7 / 17

 

Part 2:

 

You must choose December 1st Times magazine.

There are C(17,3) = 17·16·15 / 3! = 680 ways to choose the other three magazines.

Thus the probability of getting the December 1st Times magazine among the four drawn is

680 / 3060 = 2 / 9