stats chapter 4 section 6

Question

A fan of country music plans to make a custom CD with 12 of her 30 favorite songs. How many different combinations of 12 songs are possible? Is it practical to make a different CD for each possible combination?
How many different combinations of 12 songs are possible?

Answer 1

There are 30 available songs and we want 12 of them. It is a combination, because once we choose 12 song, the order of the songs on the disc is not important.

₃₀C_{12 =30!/[(30-12)! x 12!]}

         =86,493,225

 

We can choose 12 songs out of 30 in 86,493,225 ways.