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1. Solve: 6C3

2. Which is not a combination?

1. 6C3 = (6!)/(3!(6-3)!) = (6x5x4)/(3x2x1) = 20

2. "4 choose 5" is not a combination because it violates the rule that you cannot choose more items than are available in the set.

Did you know?

"Did you know that in mathematics, combinations are a way to count the number of ways to select a certain number of items from a larger set without regard to their order? For example, to solve the expression 6C3, you would find the number of ways to choose 3 items out of a set of 6. In this case, 6C3 is equal to 20. So, remember, combinations help us count possibilities in a non-sequential manner!" "Did you know that not all sets of items can be considered combinations? In mathematics, a combination is a selection of items where the order of the selected items does not matter. However, if the order does matter, it is called a permutation. Therefore, permutations are not considered combinations. Ensuring the distinction between combinations and permutations is important when working with counting principles and probability calculations. Stay mindful of whether the order matters or not when categorizing different scenarios!"