# Formulas For Combination

## Combination Formulas

Combination Formulas used for calculating the number of ways of selecting the items.

Formula of Combination , $^nC_r = \frac{n!}{(n-r)! r! }$

A combination is a selection of items from a set that has distinct members, such that the order of selection does not matter. Formulas for Combination is discussed on this page to help students remember all the key points last minute before exam.

### Combination Formulas

• Number of all combinations of n things, taken r at a time, is given by

nCr = $\frac{n!}{(n-r)! r! }$n!/(r!) (n-r)!

• n-combinations from a set with n elements (without repetition)

nCr = $\frac{n!}{(n-r)! r! }$

• n-combinations from a set with n elements (with repetition)

r + n – 1Cr = C (n, r)

### Points to remember in Combination Formulas

• nCn = 1
• nC0 = 1
• nCrnC(n – r)
• nC0 + nC1+ nC2+ nC3+ ……………+ nCn = 2n