Amy has 5 CDs that she is going to away. She lets her best friend choose 3 of the 5 CDs. How many different groups of 3 CDs arepossible

10

Step-by-step explanation:

5C3 = 10

In grouping, order doesn't matter

So no arrangement, just selections

Explanation:

If order mattered, then there would be 5*4*3 = 20*3 = 60 different permutations. Note how I started at 5 and counted down by one until I had three values to multiply, since Amy's friend picks 3 CDs. For the first slot she has 5 items to choose from, then the second slot is 4 items because she cant select the first item again, and then 3 choices for the third slot (it's a coincidence that we have the value 3 in slot 3).

If order mattered, then we would stop here. However, order does not matter. A set like {A,B,C} is the same as {B,C,A}. There are 3! = 3*2*1 = 6 ways to arrange any set of 3 items. So we overcounted by a factor of 6. Meaning we have to divide by 6 to correct this overcounting.

60/6 = 10

There are 10 combinations that can be formed if there are 5 items to choose from and you have 3 slots to fill. Here are all of the 10 different combinations: