# Permutations and Combinations Worksheet

This worksheet contains the collection practice problems for permutation & combination.

Worksheet for Permutation
The number of arrangements that can be made out of n things taking r at a time is called the number of permutations of n things taken r at a time.
1. npr = n (n - 1) (n - 2 ..... (n - (r - 1))
2. npr = n! / (n - r)!
3. npn = n!
4. np0 = 1
5. The number of mutually distinguishable permutations of n things, taken all at a time, of which p are alike of one kind, q alike of second kind such that p + q = n is n! /p!q!
6. The number of circular permutations of n distinct objects is (n - 1)!
7. If there are n things and if the direction is not taken into consideration, the number of circular permutation is (n - 1)! /2

Worksheet for Combination:
A selection of any r things out of n things is called Combination of n things r at a time.
1. nCr = n! /r!(n - r)!
2. nCr = nPr /r!
3. nCn = 1
4. nC0 = 1
5. nCr = nCn - r
6. If x and y are non-negative integers such that x + y = n then nCx = nCy .
7. If n and r are positive integers such that r <= n, then nCr + nCn - r = n + 1Cr .
8. If n and r are positive integers such that 1 <= r <= n, then nCr = (n / r) (n - 1)C(r - 1)
9. For any positive integers x and y nCx = nCy => x = y (or) x + y = n.

Difference between Permutation and combination
1. In a combination only selection is made whereas in a permutation not only a selection is made but also as arrangement in a definite order is considered.
2. Usually the number of permutation exceeds the number of combinations.
3. Each combination corresponds to many permutations.

When you try such calculations on your own, use permutation & combination calculator to verify the results of your calculations.

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