Answer to Question #132798 in Statistics and Probability for yaho

Question

James owns 8 different mathematics books and 4 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?

Answer 1

The selection and arrangement of first 3 positions of the math books in the shelf can be done in the following number of ways,

8C3*3! which means selecting 3 math books from 8 books and then arranging them in 3! ways.

Similarly the selection and arrangement of the last 2 positions of the computer science books in the shelf can be done in the following number of ways,

4C2*2!

Hence the positioning of 3 math books and 2 computer science books can be done in the following number of ways

8C3*3!*4C2*2! = 4032 WAYS.