Permutations & Combinations

Formulas are organized based on their importance in the CAT exam.
1 Committee with Equal Representation
2 Circular Permutation of n distinct objects
3 Combination of n distinct objects taken r at a time
4 Permutation of n distinct objects taken r at a time
5 Factorial
6 Division into Distinct Groups (Multinomial Coefficient)
7 Addition Principle of Counting
8 Division into Identical Groups
9 Number of Permutations of $$n$$ Distinct Objects
10 Permutation of Repeated Objects
11 Basic Properties of Combinations
12 Relation Between Consecutive Combinations
13 Selection
14 Sum of Even-Indexed Combinations
15 Permutations with Restrictions
16 Permutations with Identical Objects Together
17 Permutation of $$r$$ Objects
18 Fundamental Principle of Counting
19 Sum of Squares of Combination Coefficients
20 Permutations with Repetition Allowed
21 Number Formation Without Repetition
22 Permutations with Repetition of Identical Objects
23 Sum of All Combinations
24 Sum of Products of Two Combination Terms
25 Permutations with Objects Not Together
26 Inclusion-Exclusion for Counting
27 Ratio of Consecutive Permutations
28 Selection of at Least One Object
29 Men and Women in a Row
30 Positive Integer Solutions
31 Distribution of Distinct Objects
32 Selection and Arrangement Together
33 Number of Line Segments from $$n$$ Points
34 Number of Permutations with No Repetition
35 Number of Even Divisors
36 Number of Derangements
37 Objects Together in a Circular Arrangement
38 Non-Negative Integer Solutions with Upper Restrictions
39 Selection with at Least One from a Particular Group
40 Selection of Exactly $$r$$ Objects
41 Relation Between Even and Odd Combinations
42 Arrangements with Two Specified Objects Together
43 Circular Permutation
44 Combination with Repetition (Stars and Bars)
45 Number of Odd Divisors
46 Derangements
47 Distribution of Distinct Objects with Non-Empty Groups
48 Men and Women Alternating
49 Circular Arrangement with Two Specified Objects Not Together
50 Permutations with At Least One Restriction
51 Number of Divisors
52 Circular Arrangement with Two Specified Objects Together
53 Circular Permutation with Clockwise and Anticlockwise Equivalence
54 Permutations with Objects Together
55 Choosing at Least One from Each Group
56 Committee Formation
57 Restricted Selection
58 Arrangements with a Fixed Object at an End
59 Choosing Exactly $$r$$ from Multiple Groups
60 Number Formation With Repetition
61 Selection with Exactly One from a Particular Group
62 Complementary Counting
63 Circular Alternating Arrangement
64 Permutation of n objects with repetitions
65 Number of Diagonals of a Polygon
66 Relation Between Permutations and Factorials
67 Greatest Value of ${}^nC_r$
68 Sum of Odd-Indexed Combinations
69 Identical Objects in Distribution ## Formula
70 Ranking Problems
71 Distribution of Identical Objects
72 Inclusion-Exclusion for Bounded Sum
73 Arrangements with Two Specified Objects at the Ends
74 Sine of Sum of Three Angles
75 Objects Not Together in a Circular Arrangement
76 Committee with at Least One from Each Group
77 Number of Regions Formed by Chords of a Circle
78 Selection with No Object from a Particular Group
79 Number of Solutions of a Linear Equation
80 Ratio of Consecutive Combination Terms
81 Permutation
82 Selection with Repetition
83 Relation Between Permutation and Combination
84 Arrangements with Two Specified Objects Not Together
85 Number of Triangles from $$n$$ Points
86 Alternating Sum of Combinations
87 Weighted Combination Sum
88 Fundamental Principle of Counting