Request a call back

# Permutations and Combinations

Permutations and Combinations PDF Notes, Important Questions And Synopsis

## Permutations And Combinations PDF Notes, Important Questions and Synopsis

SYNOPSIS

1. 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 byP(n, r) = , where 0 ≤ r ≤ nn →  number of things to choose fromr → 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 byC(n, r) = , where 0 ≤ r ≤ n →  number of things to choose fromr →  number of things we choose! →  factorial
2. 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
1.  When ‘k’ particular things are always to be included.
Number of permutations: 2. When a particular thing is always to be included (k = 1).
Number of permutations: 3. When ‘k’ particular things are never included.
Number of permutations: 4.  When a particular thing is never included.
Number of permutations: 5. When ‘l’ particular things always come together.
Number of permutations: (n - l + 1)!  l!
6. 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 ←  Taking 2 at a time ii.  Permutations without repetition (No repetition, order matters)Out of ←  Taking 2 at a time 3.Combination

 i Total number of combinations Ways of selecting one or more things at a time.Number of combinations: When ‘k1’ alike objects of one kind, ‘k2’ alike objects of the second kind … ‘kn’ alikeobjects of the nth kind.Number of combinations: When ‘k1’ alike objects of one kind, ‘k2’ alike objects of the second kind … ‘kn’ alikeobjects of the nth kind and rest ‘p’ elements are different.Number of combinations: ii  Combinations under restriction When ‘k’ particular things are always to be includedNumber of combinations: When a particular thing is always to be included (k = 1)Number of combinations: When ‘k’ particular things are never includedNumber of combinations: When ‘k’ particular things never come togetherNumber of combinations: 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 ## JEE Main Video Lectures By Experts

VIEW ALL
JEE Main - Maths
do Asked by krrishgarg967 | 07 Jan, 2023, 11:31: PM ANSWERED BY EXPERT
JEE Main - Maths
(A) 72 993. How many five-digit even numbers can be formed from the dights, 2,3,4,7 and 8, the digs are not repeated O (8) 36 © (c) 120 O (0) 54
Asked by abhishekssstays | 17 Dec, 2022, 05:00: PM ANSWERED BY EXPERT
JEE Main - Maths
velocity Asked by varshitchouhan8 | 08 May, 2022, 08:48: PM ANSWERED BY EXPERT
JEE Main - Maths
number of ways of selecting three consecutive objects out of 15 objects distinct place around a circle ANSWERED BY EXPERT
JEE Main - Maths
7c1
Asked by panchalbhavesh372 | 16 May, 2021, 10:50: AM ANSWERED BY EXPERT
JEE Main - Maths
Permutations and combinations Asked by navyaankita121993 | 08 Feb, 2021, 08:40: PM ANSWERED BY EXPERT
JEE Main - Maths
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
Asked by alicianary | 02 Feb, 2020, 08:30: PM ANSWERED BY EXPERT
JEE Main - Maths
Solve this with explanation plz Asked by vishakhachandan026 | 12 Oct, 2019, 06:30: PM ANSWERED BY EXPERT
JEE Main - Maths
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 Asked by aaryannagpal2003 | 02 Oct, 2019, 06:52: PM ANSWERED BY EXPERT
JEE Main - Maths
Plz solve the attached image, Ans: c Asked by vishakhachandan026 | 25 Jun, 2019, 07:02: AM ANSWERED BY EXPERT