Question

Steve wants to download a selection of new music. How many ways can Steve select three rock songs, four alternative songs, andthree rap songs from a list of eight rock songs, five alternative songs, and six rap songs?00>>There areways that Steve can select his songs.х6ERCheckSave For LaterSubmit Assignment

Answer 1

This is a question on combinations.

Combinations are applied to find the number of unique outcomes that are obtainable.

To select r from a sample space of n, the number of ways that r can selected from n is given as:

$^nC_r$

In this case,

n = number of total songs

r = number of songs chosen at one time.

Therefore, the number of ways that 3 rock songs can be chosen from 8 is given as:

$^8C_3=\frac{8!}{(8-3)!3!}=\frac{8!}{5!3!}=\frac{8\times7\times6\times5!}{5!\times3!}=56$

The number of ways that 4 alternative songs can be chosen from 5 is given as:

$^5C_4=\frac{5!}{(5-4)!4!}=\frac{5!}{1!4!}=\frac{5\times4!}{4!\times1!}=5$

The number of ways that 3 rap songs can be chosen from 6 is given as:

$^6C_3=\frac{6!}{(6-3)!3!}=\frac{6!}{3!3!}=\frac{6\times5\times4\times3!}{3!\times3!}=20$

Therefore, The total number of ways that Steve can select his songs is:

$56\times5\times20=5600\text{ ways}$