JEE Maths Permutations and Combinations
Permutations And Combinations PDF Notes, Important Questions and Synopsis
SYNOPSIS
 Fundamental Principle of Counting
 Permutation is the number of ways to arrange things.
Eg: Password is 2045
(order matters)  It is denoted by P(n, r) and given by
P(n, r) =, where 0 ≤ r ≤ n
n → number of things to choose from
r → number of things we choose
! → factorial
 Combination is the number of ways to choose things.Eg: A cake contains chocolates, biscuits, oranges and cookies.
(Order does not matter)  It is denoted by C(n, r) and given by
C(n, r) =, where 0 ≤ r ≤
n → number of things to choose from
r → number of things we choose
! → factorial
 Permutation is the number of ways to arrange things.
 Permutation
If n is the number of distinct things and r things are chosen at a time.
i. Permutation of objects when all are not distinct:
Permutation = , → Number of things among ‘n’ which are alike of rth type.
ii. Circular permutation
1. When clockwise and anticlockwise arrangements are different:
Number of permutations: (n  1)!
2. When clockwise and anticlockwise arrangements are the same:
Number of permutations:
iii. Permutation under restrictions
Selecting and arranging r distinct objects from n
 When ‘k’ particular things are always to be included.
Number of permutations:  When a particular thing is always to be included (k = 1).
Number of permutations:  When ‘k’ particular things are never included.
Number of permutations:  When a particular thing is never included.
Number of permutations:  When ‘l’ particular things always come together.
Number of permutations: (n  l + 1)! ⨯ l!  When ‘l’ particular things never come together.
Number of permutations: n!  (n  l + 1)! ⨯ l!
i. Permutations with repetition Number of permutations: ^{n}P_{r}= n^{r} (Repetition, order matters)
Out of ← Taking 2 at a time 
ii. Permutations without repetition
(No repetition, order matters) Out of ← Taking 2 at a time 
3.Combination


ii Combinations under restriction


i. Combination with repetition Formula: (Repetition, order does not matter) Out of _{ }← Taking 2 at a time 
ii. Combination without repetition Formula: (No repetition, order does not matter) Out of ←Taking 2 at a time 
Videos
JEE Class Revise
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