eguruchela

Permutation and Combination Calculator


Calculate the number of possible permutations and combinations for given a set of n elements and r

Number of sample points in set n :
Number of sample points r :

 

Results:

Permutation:
Combination:

All possible arrangements of a grouping of things, where the order is important is called permutation. A Grouping of things, in which the order does not matter is called Combination. Given Calculator finds the Permutation and combination of the given numbers.

Calculates the given value uing following formula :

Permutation: nPr = n! / (n-r)!
Combination: nCr = nPr / r!

Example

1. Find the Permutation for Number of sample points in set n = 7 and Number of sample points r = 4.

$$ nPr = P(n,r) = \frac{n!}{(n-r)!} $$ $$ =\frac{7!}{(7-4)!}$$ $$ =\frac{7!}{(3)!} $$ $$ =\frac{5040}{6} $$ $$ =840 $$

2. Find the Combination for Number of sample points in set n = 7 and Number of sample points r = 4.

$$ nPr = P(n,r) = \frac{n!}{(n-r)!} $$ $$ nCr = \frac{nPr}{r!} $$ $$ nPr =\frac{7!}{(7-4)!}$$ $$ nPr =\frac{7!}{(3)!} $$ $$ nPr =\frac{5040}{6} $$ $$ nPr =840 $$

now to calculate nCr:

$$ nCr =\frac{840}{(4)!} $$ $$ nCr =\frac{840}{24} $$ $$ =35 $$