Question

You are choosing a CD from your friend’s music collection. You can choose 1 of 4 country CDs, 1 of 3 soul CDs, or 1 of 5 pop CDs. How many ways can you choose a CD?

Question 2 options:

10


12


48


60

Answer 1

the answer is 12 i have answered a question just like dis disrigard the 1 and the genres just add the total number of cds

Answer 2

We have been given that we can choose 1 of 4 country CDs, 1 of 3 soul CDs, or 1 of 5 pop CDs.

We need to figure out number of ways in which we can choose 1 CD of each kind from available options.

To figure out number of ways in which we can choose 1 CD of each kind we will use combinations.

First of all we will figure out number of ways of choosing 1 CD out of 4 country CDs, then we will figure out number of ways of choosing 1 CD out of 3 soul CDs. We will also determine number of ways of choosing 1 CD out of 5 pop CDs.

Number of ways of choosing 1 CD out of 4 country CDs =

`(_(1)^(4)\textrm{c})=(4!)/(3!1!)=(4\cdot 3!)/(3!)=4`

Number of ways of choosing 1 CD out of 3 soul CDs =

`\\(_(1)^(3)\textrm{c})=(3!)/(2!1!)=(3\cdot 2!)/(2!)=3`

Number of ways of choosing 1 CD out of 5 pop CDs =

`\\(_(1)^(5)\textrm{c})=(5!)/(4!1!)=(5\cdot 4!)/(4!)=5`

Therefore total number of ways to select 1 CD is
`4\cdot 3\cdot 5=60\text{ways}`