Julie owns 8 different mathematics books and 5 different computer science books and wish to fill 5 positions on a shelf. if the first 3 positions are to be occupied by math books and the last 2 by computer science books, in how many ways can this be done?

Each number being multiplied represents the number of choices of books for each slot on the shelf.

8 x 7 x 6 x 5 x 4 = 6720 ways

first 3 slots 8, 7,6 choices of math ... number goes down by one because the previous slot was filled. last 2 slots 5, 4 choices of science books