Numbers of different arrangements that
can be made by taking some or all the
items are called permutations of those
Numbers of different groups
that can formed by selecting some or all
the items are called combinations of those
When these are ‘n’ items and we make arrangements of them
taking ‘r’ at a time we get nPr arrangements.
nPn means numbers of ‘n’ things taken ‘r’ at a time.
Formula : nPr = n( n-1 )( n-2 )…….( n-r+1 )
= n ! _
( n-r )!
1. Permutations of ‘n’ different things taken ‘r’ at a time
Number of arrangements = nPr
2. Permutation where a particular item is to be in a specified
3. Circular Permutation
when there are ‘n’ objects they can be arranged
in ( n-1 ) ways.
4. Permutations of things not all different
p! q! r!
5. Permutation with repetition (or replacement)
nCr means the number of combination, without repetition of
‘n’ things taken ‘r’ at a time.
Formula: nCr = n !____
r! ( n-r )!
Example 1 :
Find who many way a cricket team
containing 11 players can be formed from 15 high
class players available.
Ans: n= 15 and r=11
Number of ways of forming cricket team = 15C11
Permutation mainly deals with arrangements of a
given set of items.
And Combination deals with selection of
items from a group of items