Permutations & Combinations

Formulas are organized based on their importance in the CAT exam.
1 Circular Permutation of n distinct objects
2 Committee with Equal Representation
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 Permutation of Repeated Objects
10 Basic Properties of Combinations
11 Selection
12 Sum of Even-Indexed Combinations
13 Permutations with Identical Objects Together
14 Permutation of $$r$$ Objects
15 Relation Between Consecutive Combinations
16 Permutations with Restrictions
17 Fundamental Principle of Counting
18 Sum of Squares of Combination Coefficients
19 Permutations with Repetition Allowed
20 Number Formation Without Repetition
21 Permutations with Repetition of Identical Objects
22 Sum of Products of Two Combination Terms
23 Permutations with Objects Not Together
24 Inclusion-Exclusion for Counting
25 Ratio of Consecutive Permutations
26 Selection of at Least One Object
27 Sum of All Combinations
28 Men and Women in a Row
29 Positive Integer Solutions
30 Distribution of Distinct Objects
31 Selection and Arrangement Together
32 Number of Permutations of $$n$$ Distinct Objects
33 Number of Line Segments from $$n$$ Points
34 Number of Permutations with No Repetition
35 Number of Even Divisors
36 Non-Negative Integer Solutions with Upper Restrictions
37 Objects Together in a Circular Arrangement
38 Selection of Exactly $$r$$ Objects
39 Relation Between Even and Odd Combinations
40 Arrangements with Two Specified Objects Together
41 Circular Permutation
42 Selection with at Least One from a Particular Group
43 Number of Derangements
44 Combination with Repetition (Stars and Bars)
45 Number of Odd Divisors
46 Distribution of Distinct Objects with Non-Empty Groups
47 Circular Arrangement with Two Specified Objects Not Together
48 Permutations with At Least One Restriction
49 Number of Divisors
50 Committee Formation
51 Men and Women Alternating
52 Circular Arrangement with Two Specified Objects Together
53 Circular Permutation with Clockwise and Anticlockwise Equivalence
54 Choosing at Least One from Each Group
55 Permutations with Objects Together
56 Restricted Selection
57 Choosing Exactly $$r$$ from Multiple Groups
58 Circular Alternating Arrangement
59 Permutation of n objects with repetitions
60 Derangements
61 Selection with Exactly One from a Particular Group
62 Arrangements with a Fixed Object at an End
63 Number Formation With Repetition
64 Complementary Counting
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