Here is the problem:
You have a book collection that consists of 20 horror novels, 15 romance novels, and 25 mystery novels. You randomly pick 4 books to read during a long trip. What is the probability that you pick at least one book of each type?
Please tell me if I did this right:
I got 1,500/1,711 (simplified from 472,500/487,635).
- I got 487,635 by finding the total number of combinations.
- I found the total # of combinations by doing 38C4. (38!/34!*4!=487,635)
- I got 472,500 by finding the number of combinations of 4 books where there is at least one of each book.
- I did this by adding (20C1*15C1*25C2)+(20C1*15C2*25C1)+(20C2*15C1*25C1).
- This simplifies to (20*15*25*24)+(20*15*14*25)+(20*19*15*25) = 180,000+142,500+105,000 = 427,500.