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Theory of Permutation and Combination

Defining Permutations: Permutation is defined as the different arrangements of a given numbers of things by taking some or all at a time.

Example: arrangement of three letters a, b, c by taking two a time (ab, ba, ac, ca, bc, cb)

Numbers of Permutations: If total number of things n, taken r at a time

nPr =n(n-1)(n-2)…….(n-r+1) = n!/n-r!

Example 6P4 = 6*5=30

Results: Number of all permutations of n things, taken all at a time = n!

If total n object

P1 are alike of one kind

P2 are alike of one kind

Pr are alike of one kind


Then number of permutation of these n objects


Defining Combinations: Each of different groups or selections which can be formed by taking some or all of a number of objects.

Numbers of Combinations

N total things, taken r at a time

ncr= n! / (r!)(n-r!)



Important Result

ncr= ncn-r

Related Topics: Counting Principles, Permutations, Circular Permutations, Combinations, Restricted Selections/ Arrangements