Monday, 3 July 2017

Permutations and Combinations I : Important Permutations and Combinations Formulas and Concepts

In this post, we will discuss important permutations and combinations formulas to solve permutations and combinations questions in Bank Exams
Permutations and Combinations Formulas
Permutation and Combination questions though complex, appear in all Bank Exams.These questions carry 1- 5 marks. Permutations and Combinations Questions can be easily solved in few seconds using Permutations and Combinations Formulas. In this post, we will discuss important permutations and combinations formulas and concepts that will help you solve permutations and combinations questions and save time in bank exams.

Fundamental Counting Principles

Fundamental Principle of Addition:
If one action can be done in ‘m’ different ways and another action can be done in ‘n’ different ways, independent of the first one, then either of the two actions can be done in
(m + n) ways.

Example:
5 different chocolates (C1, C2, C3, C4 and C5) [We can select a chocolate in 5 different ways]
6 different fruits (F1, F2, F3, F4, F5 and F6) [We can select a Fruit in 6 different ways]
Chances of selecting either a chocolate or a Fruit = 5 + 6 = 11 ways.

Both the options are independent in nature i.e. when we select a chocolate it doesn’t depend on fruit and likewise, when we select a fruit, it doesn’t depend on chocolates.

Fundamental of Multiplication:
If one action can be done in ‘m’ different ways and another action can be done in ‘n’ different ways, independent of the first one, then both the actions together can be done in (m x n) ways.

Example: Town A to Town B => 3 different routes
Town B to Town C => 2 different routes
Permutations and Combinations Formulas
If the person has to travel from Town A to Town C how many ways will he have? 
m x n = 3 x 2 = 6 ways. 

Factorial:
Factorial ‘n’ or ‘n’ factorial is defined as the product of first n natural numbers. It is denoted by n! (or) Ln.

n! = 1 x 2 x 3 x 4 x 5 …… x n

Example: 1! = 1
2! = 1 x 2 = 1! x 2 = 2
3! = 1 x 3 = 2! x 3 = 6
4! = 1 x 4 = 3! x 4 = 24

Exception* 
Permutations and Combinations Formulas

Formula: 
Permutations and Combinations Formulas
Permutation:
It is an arrangement which can be done using some or all of a given number of objects.

Example: The number of permutations of 3 objects a, b, c taken 2 at a time is ab, bc, ca, ba, cb and ac.

Note: Sequence/order is important.

Therefore, Permutation = Arrangement
Number of permutations of ‘n’ different objects taken ‘r’ at a time is given as
Permutations and Combinations Formulas
Combinations:
It is a grouping or selection, which can be done using some or all of the given objects.
 
Example: The number of combination of 3 objects a, b, c taken 2 at a time are ab, bc, ca.
Note: Sequence is not important.

Therefore, Combination = Selection

Number of combinations of ‘n’ different objects taken ‘r’ at a time is given as,
Permutations and Combinations Formulas
This was the basic introduction to the topic of permutations and combinations. In our next post, we will discuss few basic and advanced permutation and combination questions which will help you save time in bank exam.

Do write in the comment section how this list of Permutations and Combinations Formulas help you understand Permutation and Combinations Questions.

Stay tuned for Permutation and Combinations Questions.
Permutations and Combinations Formulas
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