Combination

Permutations count ordered lists. Think of a race—first place matters! But in many cases, order doesn't matter. For instance, in a card hand, the order you receive the cards is irrelevant. When order is unimportant, we use combinations instead of permutations.

How to compute the number of Combinations for a given set of objects

To compute the number of permutations for a given set of objects, you can use the formula:

nCr = n!/r!(n-r)!

where n is the total number of objects, r is the number of objects to arrange, and ! denotes factorial. For example, if you want to arrange 3 objects from a set of 4, you calculate:

4C3 = 4!/3!(4-3)! = 4!/3!1! = 4

This formula accounts for the order of arrangement, making it suitable for scenarios where the sequence matters.