Updated On : March 31, 2022

Permutation and Combination are the ways to represent a group of objects by selecting them in a set and forming subsets. It defines the various ways to arrange a certain group of data. When we select the data or objects from a certain group, it is said to be permutations, whereas the order in which they are represented is called combination. Both concepts are very important in Mathematics.

In mathematics, permutation relates to the act of arranging all the members of a set into some sequence or order**. **In other words, if the set is already ordered, then the rearranging of its elements is called the process of permuting. Permutations occur, in more or less prominent ways, in almost every area of mathematics. They often arise when different orderings on certain finite sets are considered.

The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter**.** In smaller cases, it is possible to count the number of combinations. Combination refers to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used. Permutation and Combination Class 11 is one of the important topics which help in scoring well in Board Exams.

**Formula of Permutation is:**

A permutation is the choice of r things from a set of n things without replacement and where the order matters.

**n****P****r**** = (n!) / (n-r)!**

**Formula of Combination is:**

A combination is the choice of r things from a set of n things without replacement and where order doesn't matter.

**ɴCᵣ = (n/r) = ɴPᵣ / r! = n! / r! (n - r)!**

In this article, you will get to know how to solve permutation and combination questions for Aptitude Exams

Look at the questions mentioned below to know how to solve Permutation and Combination Questions. We have mentioned all types of questions below starting from easy then moderate and after that hard level of questions. This will help you to know how you can solve Permutation and Combination questions of any level easily.

Download Free Study Material for IPMAT and DU JAT Exams by SuperGrads

**Easy Level**

**Question 1: **How many numbers are there between 100 and 1000 such that at least one of their digits is 5?

(a) 215

(b) 225

(c) 125

(d) 252

**Question 2: **For a set of five true or false questions, no student has written the all correct – answer and no two students have given the same sequence of answers. What is the maximum number of students in the class for this to be possible?

(a) 15

(b) 31

(c) 32

(d) 63

** Question 3: **A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of February calendars should it prepare to serve for all the possibilities in the future years?

(a) 7

(b) 21

(c) 14

(d) 49

**Question 4: **There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 5 each?

(a) 1000

(b) 8000

(c) 1200

(d) 4000

**Question 5: **In how many ways 6 letters can be posted in 5 letter boxes available in the locality?

(a) 6!

(b) 6 ^ 5

(c) 5!

(d) 5 ^ 6

** Question 6: **There are 5 letters and 5 directed envelopes. Find the number of ways in which the letters can be put into the envelopes so that all are not put in directed envelopes?

(a) 32

(b) 31

(c) 119

(d) 120

**Question 7: **12 villages in a district are divided into 3 zones with 4 villages per zone. The telephone department of the district intends to connect the villages with telephone lines such that every two villages in the same zone are connected with three direct lines and every two villages belonging to different zones are connected with two direct lines. How many direct lines are required?

(a) 112

(b) 120

(c) 150

(d) 132

**Question 8: **How many 3 digits numbers which are divisible by 3 can be formed using 2, 3, 4 and 5?

(a) 22

(b) 6

(c) 16

(d) 81

**Question 9: **How many 4 digit numbers which are divisible by 4 can be formed using 0, 1, 2, 3, 4, 5 and 6?

(i) Repetition Allowed

(ii) Repetition not Allowed

(a) 320, 124

(b) 720, 240

(c) 208, 504

(d) 588, 208

March 31, 2022

Permutation and Combination are the ways to represent a group of objects by selecting them in a set and forming subsets. It defines the various ways to arrange a certain group of data. When we select the data or objects from a certain group, it is said to be permutations, whereas the order in which they are represented is called combination. Both concepts are very important in Mathematics.

In mathematics, permutation relates to the act of arranging all the members of a set into some sequence or order**. **In other words, if the set is already ordered, then the rearranging of its elements is called the process of permuting. Permutations occur, in more or less prominent ways, in almost every area of mathematics. They often arise when different orderings on certain finite sets are considered.

The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter**.** In smaller cases, it is possible to count the number of combinations. Combination refers to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used. Permutation and Combination Class 11 is one of the important topics which help in scoring well in Board Exams.

**Formula of Permutation is:**

A permutation is the choice of r things from a set of n things without replacement and where the order matters.

**n****P****r**** = (n!) / (n-r)!**

**Formula of Combination is:**

A combination is the choice of r things from a set of n things without replacement and where order doesn't matter.

**ɴCᵣ = (n/r) = ɴPᵣ / r! = n! / r! (n - r)!**

In this article, you will get to know how to solve permutation and combination questions for Aptitude Exams

Look at the questions mentioned below to know how to solve Permutation and Combination Questions. We have mentioned all types of questions below starting from easy then moderate and after that hard level of questions. This will help you to know how you can solve Permutation and Combination questions of any level easily.

Download Free Study Material for IPMAT and DU JAT Exams by SuperGrads

**Easy Level**

**Question 1: **How many numbers are there between 100 and 1000 such that at least one of their digits is 5?

(a) 215

(b) 225

(c) 125

(d) 252

**Question 2: **For a set of five true or false questions, no student has written the all correct – answer and no two students have given the same sequence of answers. What is the maximum number of students in the class for this to be possible?

(a) 15

(b) 31

(c) 32

(d) 63

** Question 3: **A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of February calendars should it prepare to serve for all the possibilities in the future years?

(a) 7

(b) 21

(c) 14

(d) 49

**Question 4: **There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 5 each?

(a) 1000

(b) 8000

(c) 1200

(d) 4000

**Question 5: **In how many ways 6 letters can be posted in 5 letter boxes available in the locality?

(a) 6!

(b) 6 ^ 5

(c) 5!

(d) 5 ^ 6

** Question 6: **There are 5 letters and 5 directed envelopes. Find the number of ways in which the letters can be put into the envelopes so that all are not put in directed envelopes?

(a) 32

(b) 31

(c) 119

(d) 120

**Question 7: **12 villages in a district are divided into 3 zones with 4 villages per zone. The telephone department of the district intends to connect the villages with telephone lines such that every two villages in the same zone are connected with three direct lines and every two villages belonging to different zones are connected with two direct lines. How many direct lines are required?

(a) 112

(b) 120

(c) 150

(d) 132

**Question 8: **How many 3 digits numbers which are divisible by 3 can be formed using 2, 3, 4 and 5?

(a) 22

(b) 6

(c) 16

(d) 81

**Question 9: **How many 4 digit numbers which are divisible by 4 can be formed using 0, 1, 2, 3, 4, 5 and 6?

(i) Repetition Allowed

(ii) Repetition not Allowed

(a) 320, 124

(b) 720, 240

(c) 208, 504

(d) 588, 208