Combination

A combination counts the number of possible selections when order does not matter.

What is a combination?

A combination refers to the selection of items from a larger set where the order of selection is irrelevant. Unlike permutations, rearranging the same elements does not create a new outcome.

Combination formula

The number of combinations of r items selected from n distinct items is:

nCr = n! / [ r! (n − r)! ]

Example

Suppose you have 5 students and want to form a committee of 2:

AB = BA (same group)

Number of combinations = 5C2 = 10

When should combinations be used?

Use combinations whenever the order of items does not affect the result, such as forming groups, selecting samples, or choosing lottery numbers.

Combination vs permutation

Combinations ignore order, while permutations consider order. Choosing the correct method is essential for accurate probability calculations.

Why are combinations important?

Combinations are central to probability theory, statistics, and data analysis, especially in distribution calculations.