Depending on your sample size, with your duplicates, you will have different Combinations
Coins Example
How many sums of money can you create with: 1 penny. 1 nickel. - 3 combinations 1 penny, 1 nickel, 1 dime. - 7 combinations 2 penny, 1 dime. - 5 combinations 3 penny, 1 dime. - 7 combinations
Case 1:
For each coin, we either chose to include it in the sum, or not include it in the sum. For 1 penny, 1 nickel. 2 choices * 2 choices = 4. but, we cannot have a sum of 0, so subtract 1 = 3.
Case 3:
There are 2 pennies and 1 dime.
For the 2 pennies, group them and calculate the combinations.
Either we pick 2, we pick none or we pick one.
Then, with the combinations of the dime, there are only 2.
3 * 2 - 1 = 5