# Permutation and combination formulas

**Permutation and combination formulas**

*Permutation* is a arrangement of objects or symbols in distinguishable sequences. Combination can be define as a selection of some or all of the number of different objects. *Combination* is a un-ordered collection of unique sizes.

Some of the important **formulas of permutation and combination** are listed below:-

[**Note**: factorial n = the product of first ‘n’ natural numbers it is denoted by n! ]

i.e. n! = n(n – 1) (n – 2) …………. 3.2.1. Ex. 5! = 5 * 4 * 3 * 2 * 1 = 120 0! = 1

**a**. Number of permutations of ‘n’ different things taken ‘r’ at a time is given by:

**b**. Number of permutations of n things, taken ‘r’ at a time when each things be repeated r-times is given by =n’.

**c**. Number n-thing taken all at a time, in which ‘p’ are of one type, ‘q’ of them are of second type, ‘r’ of them are of third type, and rest are all different is given by =

**d**. There are two case of circular permutations:

i. If clockwise and anti-clock-wise orders are different, and then total number of circular-permutations is given by: (n – 1)!

ii. if clock-wise and anti-clock-wise orders are taken as not different, then total number of circular-permutations is given by:

**e**. Total number of combinations of n object taken r at a time is denoted by C(n, r) and defined by

[**Note**: C (n, r) = C (n, n – r)]

**f.** Restricted – combinations

i. Number of combinations of ‘n’ different things taken ‘r’ at a time, when ‘p’ particular things are always included = C (n-p, r – p)

ii. Number of combinations of ‘n’ different things, taken ‘r’ at a time, when ‘p’ particular things to be excluded = C (n – p, r)

Related posts:

- Compound Interest Formulas Compound Interest is a method of determining the interest or...
- Ratio and Proportion Formulas As you know Ratio is a relation between two quantities...
- Algebraic Formulas Algebra is one of the most basic part of mathematics...
- Sequence and Series Formulas Sequence and Series Formulas A sequence is a ordered list...
- Measurement of Angles Formulas Measurement of Angles Formulas The concept of angle is one...