Question

You want to arrange 6 of your favorite CDs along a shelf. How many different ways can you arrange the CDs, assuming that the order of the CDs makes a difference to you?

a) 720
b) 120
c) 30
d) 6

Answer 1

The correct answer is A. There are 720 different ways to arrange 6 CDs on a shelf where the order matters, calculated using the factorial function (6!).

Step-by-step explanation:

There are 720 different ways to arrange 6 CDs on a shelf where the order matters.

The problem at hand is a permutation problem because we're looking at the different ways to arrange a set of items where order is important. When arranging 'n' unique items in a specific order, the number of permutations is n!. Therefore, with 6 CDs, the number of arrangements you can make is 6! (6 factorial), which is calculated by multiplying each integer from 1 up to 6 together (6 x 5 x 4 x 3 x 2 x 1).

Calculation: 6 x 5 x 4 x 3 x 2 x 1 = 720.

This result represents the total number of permutations or different ways these CDs can be ordered on a shelf.