Today, discuss a very important topic for ibps or other bank exams i.e. “Permutation and Combination”. There are so many questions from this topic because check the analytical’s skills of the candidate. You will get **Tricks & Tips **for this subject with proper** examples. **You can also **download** these **study materials** in **PDF format**.

Contents

### What is Permutation (परमुतशन)

It means that arrangement where order of things is necessary and includes word formation, number formation, circular permutation etc.

### What is Combination (कॉम्बिनेशन)

It means that selection where order of things is not important and it involves selection of team, forming geometrical figures, distribution of things etc.

### Factorial

Factorial is defined for the positive whole numbers, not for the negative numbers.

Mathematically express, n! =n*(n-1)*(n-2)*(n-3)*……………..3*2*1

### Differences between permutation & combination

PERMUTATION | COMBINATION |

Means Arrangement | Means Selection |

Order of things is important | Order of things is NOT important |

Permutation of three things a, b and c taking two at a time are ab, ba, ac, ca,bc and cb (Order is important). | Combination of three things a,b and c taking two at a time are ab, ca and cb (Order is not important). |

^{n}P_{r} =^{n!}⁄_{(n-r)!} |
^{n}C_{r} = ^{n!}⁄_{r!(n-r)!} |

^{n}P_{n} = n! |
^{n}C_{n} = 1 |

^{n}P_{} = 1 |
^{n}C_{} = 1 |

### Permutation & Combination Notes,Tricks with Examples |Questions & Answers

Question 1: In how many different ways can the letters of the word "CHARGES" be arranged in such a way that the vowels always come together?

Solution:

The arrangement is made in such a way that the vowels always come together.

i.e., "CHRGS (AE)".

Considering vowels as one letter, 6 different letters can be arranged in 6! ways; i.e., 6! = 720 ways.

The vowels "AE" can be arranged themselves in 2! ways; i.e., 2! = 2 ways

Therefore, required number of ways = 720 x 2 = 1440 ways.

Question 2: In how many different ways can the letters of the word "CANDIDATE" be arranged in such a way that the vowels always come together?

Solution:

There are 9 letters in the given word, out of which 4 are vowels.

In the word "CANDIDATE" we treat the vowels "AIAE" as one letter.

Thus, we have CNDDT (AIAE).

Now, we have to arrange 6 letters, out of which D occurs twice.

Therefore, number of ways of arranging these letters = 6! /2! = 720 / 2 = 360 ways.

Now, AIAE has 4 letters, in which A occurs 2 times and the rest are different.

Number of ways of arranging these letters = 4! /2! = 1 x 2 x 3 x 4 / 2 = 12

Therefore, required number of words = (360 x 12) = 4320.

Question 3: How many ways are there in selecting 5 members from 6 males and 5 females, consisting 3 males and 2 females?

Solution:

This is a case of combination i.e.selecting 3 males from 6 males and 2 females from 5 females.

⇒Required number of ways = (6C3 *5C2)

⇒(6.5.4/3.2)*(5.4/2)

⇒200.

Question 4: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

Solution:

Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)

=^{7}C_{3}*^{4}C_{2}

=

=210

Number of groups, each having 3 consonants and 2 vowels = 210.

Each group contains 5 letters.

Number of ways of arranging 5 letters among themselves = 5 !

=5*4*3*2*1

=120

Required number of ways = (210 x 120) = 25200.