# 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.

### Tips and Tricks for Circular Permutation

Circular Permutation are arrangements in the closed loops.

• If clockwise and anti-clock-wise orders are different, then total number of circular-permutations is given by (n-1)!
• If clock-wise and anti-clock-wise orders are taken as not different, then total number of circular-permutations is given by $\frac{(n-1)!}{2!}$
• While Solving Typical Problems divide Problems in Small Parts then think upon it.

### 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

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