Question

For your birthday you recieved a gift certificate from a music store for three CDs. There eight you would like to have. If you select the CDs at random, how many different groups of CDs could you select

Answer 1

Answer:

56

Step-by-step explanation:

First, do you know what a CD is? ;-)

Since you will pick 3 CDs out of 8, and the order of the CDs don't import (1,2,4 is the same as 2,1,4 and 4,2,1 for example),we'll calculate the Combinations (and not the permutations). The formula for Combinations is:

$C(n,r) = \frac{n!}{(r!(n-r)!)}$

Where n is the number of elements (8 in our case) an n is the sample (3 in our case).

$C(8,3) = \frac{8!}{(3!(8-3)!)} = \frac{40320}{6 * 120} = 56$

So, there are 56 random groups of 3 you can pick from your potential 8 CDs.