Count the coins/0-1

Count the coins/0-1 is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Let say you have some coins in your wallet and you want to have a given sum.

You can use each coin zero or one time.

How many ways can you do it ?

Task

Show the result the for the following examples:

•   coins = [1, 2, 3, 4, 5] and sum = 6

•   coins = [1, 1, 2, 3, 3, 4, 5] and sum = 6

•   coins = [1, 2, 3, 4, 5, 5, 5, 5, 15, 15, 10, 10, 10, 10, 25, 100] and sum = 40

Extra

•   Show the result of the same examples when the order you take the coins doesn't matter.

•   Show an example of coins you used to reach the given sum by giving the indices of coins you have taken.