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=(8!)/((8-3)!3!)=(8!)/(5!3!)=(8*7*6*5!)/(5!*3!)=56`

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

`^5C_4=(5!)/((5-4)!4!)=(5!)/(1!4!)=(5*4!)/(4!*1!)=5`

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

`^6C_3=(6!)/((6-3)!3!)=(6!)/(3!3!)=(6*5*4*3!)/(3!*3!)=20`

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

`56*5*20=5600\text{ ways}`