Permutation and Combination

Permutation

It is the different arrangements of a given number of elements.

nPr = n! / (n — r)!

• Here nPris, No of permutations when relements are arranged out of a total of nelements.
• Eg. Let n = {A, B, C, D} and r = 2. Then the permutations are AB, AC, AD, BA, BC, BD, CA, CB, CD, DA, DB and DC.

Combination

It is the different selections of a given number of elements.

n C r = n! / [ (r !) x (n — r)! ]

and, the simplified formula is

n C r = n C (n — r)

• Here nCr is, No of combinations when r elements are selected out of a total of n elements.
• Eg. Let n = {A, B, C, D} and r = 2. Then the permutations are AB, AC, AD, BC, BD, and CD.

Note

• For permutation, AB and BA are two different things.
• For selection, AB and BA are the same.

Sample problems

Refer to the sample problems in Geeks for Geeks for better understanding.