(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

Respuesta :

Answer:

84 ways

Step-by-step explanation:

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

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

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

[tex]T = C_{7,2}*C_{4,3} = \frac{7!}{2!5!}*\frac{4!}{1!3!} = 84[/tex]

This can be done in 84 ways