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 anti-clockwise arrangements are different:
Number of permutations: (n - 1)!
2. When clockwise and anti-clockwise 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: nPr= nr (Repetition, order matters)
Out of |
ii. Permutations without repetition
![]() (No repetition, order matters) Out of |
3.Combination
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ii Combinations under restriction
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i. Combination with repetition Formula: ![]() Out of ![]() ![]() |
ii. Combination without repetition Formula: ![]() (No repetition, order does not matter) Out of ![]() ![]() |
Videos
JEE Class Revise
- Permutations and combinations
- Find the number of ways of arranging the letters of the word ramanujan in the relative position of vowels and consonants are not changed.Please answer
- Solve this with explanation plz
- Q1) The number of ways in which a 5 digit number which is divisible by 3 can be formed from the digits 0,1,2,3,4,6,7.
Q2) What are the number of ways of distributing 8 identical balls into 3 boxes, with each box containing at least 1 ball.
Q3) In image
- Plz solve the attached image, Ans: c
- In a football tournament, each team played two matches against each other.if altogether 240 matches we're played . The no. of participants team is (a) 16 (b) 18 (c) 20 (d) non of these. Please solve this question.
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