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alex41 [277]
2 years ago
10

Steve wants to download a selection of new music. How many ways can Steve select three rock songs, four alternative songs, and t

hree rap songs from a list of eleven rock songs, five alternative songs, and four rap songs?
Mathematics
1 answer:
Readme [11.4K]2 years ago
3 0

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 <em>combination formula</em> is used to solve this question.

<h3>What is the combination formula?</h3>

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

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