Question

(1 point) Mike owns 7 different mathematics books and 4 different computer science books and wish to fill 5 positions on a shelf. If the first 2 positions are to be occupied by math books and the last 3 by computer science books, in how many ways can this be done

Answer 1

84 ways

Explanation:

The order in which the books are positioned is not important, so we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

In how many ways can this be done

2 math books, from a set of 7.

3 computer science books, from a set of 4.

So

`T = C_(7,2)*C_(4,3) = (7!)/(2!5!)*(4!)/(1!3!) = 84`

This can be done in 84 ways