The formula for combination is used to find the number of ways of selecting of items from a set without being concerned about the order of selection. In simple words, combination involves the selection of objects or things out of a larger group where order doesn't matter.

 The formula for the combination will help in determining the number of possible combinations that can be produced by choosing a subset of items from a larger set. It is how many different types of possible subsets can be made from the larger set. Finally, it should be noted that the formulas applied in the permutation and combination are interconnected and are explained below.

Combination Formula

Notations in nCr Formula:

r be the size of every permutation

n is the number of elements of the set under permutation

n and r are nonnegative integers.

is the factorial operator

The formula for combination reflects the number of ways in which a sample of "r" elements can be received from a larger set of "n" distinguishable objects.

Example Question Using the Combination Formula

Question 1: Father asks his son to pick 4 items from the table. If the table has 18 things to choose, how many different responses could the son give?

Solution:

Given,

r = 4 (item subset)

n = 18 (bigger item)

Thus, simply: find "18 Choose 4"

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