# Formulas For Combination

## Formulas for Combination

Formula of Combination used for calculating the number of ways of selecting the items

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

### 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

Read Also – Tips and tricks of Combination