A musician plans to perform 8 selections. In how many ways can she arrange the musical selections?

Solution:

Combinations are also called selections. Combinations correspond to the selection of things and not their arrangement.

We do not intend to arrange things. We intend to select them.

We denote the number of unique r-selections or combinations out of a group of n objects by nC_r.

Given, a musician plans to perform 8 selections.

Number of ways = n!

Here, n = 8

Number of ways = 8!

= 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 40,320

Therefore, the number of ways of selection is 40,320.

A musician plans to perform 8 selections. In how many ways can she arrange the musical selections?

Summary:

A musician plans to perform 8 selections. In 40,320 ways she can arrange the musical selections.