Question

Steve wants to download a selection of new music. How many ways can Steve select three rock songs, four alternative songs, and three rap songs from a list of eleven rock songs, five alternative songs, and four rap songs?

Answer 1

Using the combination formula, it is found that there are 3300 ways to choose the songs.

The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.

What is the combination formula?

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

For the rock songs, we have three from a set of eleven, hence:

$C_{11,3} = \frac{11!}{3!8!} = 165$

For the alternative songs, we have four from a set of five, hence:

$C_{5,4} = \frac{5!}{4!1!} = 5$

For the rap songs, we have three from a set of four, hence:

$C_{4,3} = \frac{4!}{3!1!} = 4$

Since the songs are independent, the total number of ways is given by:

$T = 165 \times 5 \times 4 = 3300$

More can be learned about the combination formula at brainly.com/question/25821700