Worksheet for how to Calculate Permutations nPr and Combination nCr

This worksheet help you to understand how to calculate Permutation ⁿP_r and Combination ⁿC_r for n different items or symbols.

Permutations:>Permutations where the repetitions are not allowed and the order is important; the number of permutation of n distinct things taken r at a time is written as ⁿP_r. The formula to calculate it is,
ⁿP_r = n!/(n-r)!

Example:
To find permutations for n = 5, r = 3
ⁿP_r = n!/(n-r)!
= 5! /(5-3)!
= 120/2!
= 60

Combination:
The Combination is a way of selecting several items or symbols out of a larger group, where order does not matter. The Combination represented by ⁿC_r and calculated from the below formula
ⁿC_r = n!/(r!(n-r)!)

Example:
To find combination for n = 5, r = 3
ⁿC_r = n!/(r!(n-r)!)
= 5! /( 3! (5-3)!)
= 120/(6*2)
=40

Difference between permutation & combination:
Where the repetition is not allow and combination is used for selecting several symbols for larger group and the order is not a matter but in permutation the order is important.

When you try such calculations on your own, this permutation & combination calculator can be used to verify your results of calculations.