Question

You want to arrange 12 of your favorite CD's along a shelf. How many different ways can you arrange the CD's assuming that the order of the CD's makes a difference to you?

Answer 1

The number of different ways to arrange 12 CDs along a shelf, where the order matters, is 479,001,600.

Step-by-step explanation:

The number of different ways to arrange 12 CDs along a shelf, where the order matters, can be found using the concept of permutations. In this case, we have a set of 12 CDs and we need to arrange them in a specific order. The formula to calculate the number of permutations is:

n! = n * (n-1) * (n-2) * ... * 2 * 1

where n represents the number of CDs (in this case, 12). By plugging in the value into the formula, we get:

12! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

This simplifies to:

12! = 479,001,600

So, there are 479,001,600 different ways to arrange the 12 CDs along the shelf.