# Combination and Permutation Calculator

Combination and permutation formulas help you count the number of subsets of a certain size that can be created from a larger set. *Combination* refers to counting subsets in which the order of the elements is irrelevant. *Permutation* refers to counting subsets in which the order does matter, that is, subsets with the same elements but arranged differently count as different subsets.

**Combination Example:**

As an example, consider the number of ways to select 2 students out of 5 students. If the students names are A, B, C, D, and E, then there are 10 possible *combinations*: AB, AC, AD, AE, BC, BD, BE, CD, CE, and DE.

If the total number of objects is *n* and the size of the subset is *m*, then the number of combinations is written (n C m) or (^{n}_{m}). It is read "n choose m."

**Permutation Example:**

Now consider the number of ways to select 2 students out of 5 students, but the order in which you pick the students matters, for instance, one student will be the leader and the other will be the assistant. Now there are 20 possible *permutations*: AB, BA, AC, CA, AD, DA, AE, EA, BC, CB, BD, DB, BE, EB, CD, DC, CE, EC, DE, and ED.

If the total number of objects is *n* and the size of the subset is *m*, then the number of permutations is written (n P m).

**Combination and Permutation Formulas**

(n C m) = n!/(m!*(n-m)!)

(n P m) = n!/(n-m)!

The symbol ! is factorial, that is, for any non-negative integer k, k! = (k)*(k-1)*(k-2)*...*(2)*(1). When k = 0, 0! is set to equal 1. Examples of combination and permutation formulas in action:

(5 C 2) = 5!/(2!*3!)

= (5*4*3*2*1)/(2*1*3*2*1)

= (5*4*3)/(3*2*1)

= 60/6 = 10

(5 P 2) = 5!/2!

= (5*4*3*2*1)/(3*2*1)

= 5*4 = 20

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