Answer: 10
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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:
- {A,B,C}
- {A,B,D}
- {A,B,E}
- {A,C,D}
- {A,C,E}
- {A,D,E}
- {B,C,D}
- {B,C,E}
- {B,D,E}
- {C,D,E}
