Assume that there are 7 different issues of time magazine, 8 different issues of popular science, and 4 different issues of sports illustrated, including the december 1st issue, on a rack. you choose 4 of them at random.

what is the probability that you choose at least 2 of the popular science magazines?

Let the letters T, P, S represent Time, Popular Science and Sports Illustrated magazines respectively.

We have 7 T , 8 P and 4 S  .

The total number of ways of selecting 4 out of 7+8+4=19 is given by the formula:





The event " choosing at least 2 P" is the complement of the event "choosing at most 1 P"

so P(choosing at least 2 P)=1-P(choosing at most 1 P)

P(choosing at most 1 P) = P(choosing no P) + P(choosing exactly 1 P)

P(choosing no P) =  



because we are choosing all 4 from the 11 non P magazines

and 

P(choosing exactly 1 P) is 




here we modified the operations of factorials, to make use of the previous calculation. 

Thus, 

P(choosing at most 1 P) = P(choosing no P) + P(choosing exactly 1 P)=0.085+0.34=0.425

So, P(choosing at least 2 P)=1-0.0425=0.575