CAT Tutorials : Permutations & Combinations

Factorial of n: n! = n(n-1)(n-2)…3.2.1

1! = 0! = 1

Permutations refer to the different arrangements of objects by taking some or all at a time. It is denoted by nPr , where n is the total number of objects and r is the number of objects taken at a time for arrangement.

nPr = n! / (n-r)! For r < n

= n! For r = n i.e. all the objects taken at a time

If n = p1 + p2 + p3 +…+ pr , where p1, p2, p3…pr are group of similar objects


Then number of permutation of these n objects

= n! / [(p1)!.(p2)!.(p3)!.....(pr)!]


Combinations refer to the selections or different groups, which are formed by taking some or all of the number of objects. It is denoted by nCr , where n is the total number of objects and r is the number of objects taken at a time for arrangement.

nCr = n! / r!(n-r)! For r < n

= 1 For r = n i.e. all the objects taken at a time

= n For r = 1


nCr = nC(n-r)
nCr + nC(r-1) = (n+1)Cr

Note: ab and ba are two different permutations but they are same combination.