CAT Important Formulae: Part 3


Candidates preparing for the CAT 2019 examination can expect 2- 3 questions from Permutation & Combination topic in the Quantitative Section. Here are some important formulae related to Permutation & Combination.

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Factorial Notation:


Let n be a positive integer. Then, factorial n denoted n! is defined as:


n! = n(n - 1)(n - 2) ... 3.2.1.




The different arrangements of a given number of things by taking some or all at a time, are called permutations.


Number of Permutations:


Number of all permutations of n things, taken r at a time, is given by:


nPr = n(n - 1)(n - 2) ... (n - r + 1) = n!


(n - r)!





Each of the different groups or selections which can be formed by taking some or all of a number of objects is called a combination.


Number of Combinations:


The number of all combinations of n things, taken r at a time is:


nCr = n! = n(n - 1)(n - 2) ... to r factors


(r!)(n - r)! r!




nCn = 1 and nC0 = 1.


nCr = nC(n - r)