# Combination Formula

A combination formula is a  way of selecting items from a collection, such that the order of selection does not matter. The combination involves selection of objects or things out of larger group where order doesn’t matter.

The combination formula will find the number of possible combinations that can be obtained by taking a sub-set of items from a larger set. It shows how many different possible sub-sets can be made from the larger set.

The combination formula show the number of ways a sample of “r” elements can be obtained from a larger set of “n” distinguishable objects.

$\LARGE Combination = \:_{n}C_{r} = \frac{_{n}P_{r}}{n!}$
When not related to Permutation,
$\LARGE Combination = \:_{n}C_{r} = \frac{n!}{(n-r)!r!}$
Here,
n, r are non negative integers
r is the size of each permutation.
n is the size of the set from which elements are permuted.
! is the factorial operator.

### Solved Examples

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

Solution:
Given,
r = 4 (item sub-set)
n = 18 (larger item)
Therefore, simply : find “18 Choose 4”

We know that, Combination = C(n, r) = $\frac{n!}{r!(n – r)!}$

$\frac{18!}{4!(18 – 4)!}$ = $\frac{18!}{14!4!}$ = 3,060 Possible Answers

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