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 =

$(_{1}^{4}\textrm{c})=\frac{4!}{3!1!}=\frac{4\cdot 3!}{3!}=4$

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

$\\(_{1}^{3}\textrm{c})=\frac{3!}{2!1!}=\frac{3\cdot 2!}{2!}=3$

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

$\\(_{1}^{5}\textrm{c})=\frac{5!}{4!1!}=\frac{5\cdot 4!}{4!}=5$

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