Question

A computer user has downloaded 35 songs using an online file-sharing program and wants to create a CD-R with 15 songs to use in his portable CD player. If the order that the songs are placed on the CD-R is important to him, how many different CD-Rs could he make from the 35 songs available to him?

Answer 1

Explanation:

To calculate the number of different CD-Rs that the computer user can create with 15 songs from the available 35 songs, we need to calculate the number of permutations.

The formula for permutations is nPr = n! / (n - r)!, where n is the total number of items and r is the number of items taken at a time.

In this case, the computer user has 35 songs available, and they want to create a CD-R with 15 songs.

Number of permutations = 35P15 = 35! / (35 - 15)!

Calculating this:

35! / (35 - 15)! = (35 * 34 * 33 * ... * 21) / 15!

However, the factorial calculation for 35! / 15! is extensive and can be challenging to compute directly. Instead, we can simplify the expression using cancelations:

35! / (35 - 15)! = (35 * 34 * 33 * ... * 21) / (15 * 14 * 13 * ... * 1)

Many terms will cancel out:

(35 * 34 * 33 * ... * 21) / (15 * 14 * 13 * ... * 1) = 35 * 34 * 33 * ... * 21

Now, we can calculate the simplified expression:

35 * 34 * 33 * ... * 21 ≈ 5.0477859e+19

Therefore, the computer user can create approximately 5.0477859e+19 different CD-Rs with 15 songs from the available 35 songs.