NCERT Solutions for Exercise 7.1 Class 11 Maths Chapter 7 - Permutations and Combinations

# NCERT Solutions for Exercise 7.1 Class 11 Maths Chapter 7 - Permutations and Combinations

Edited By Vishal kumar | Updated on Nov 07, 2023 07:05 AM IST

## NCERT Solutions for Class 11 Maths Chapter 7 Permutations And Combinations Exercise 7.1- Download Free PDF

NCERT Solutions for Class 11 Maths Chapter 7: Permutations and Combinations Exercise 7.1- In our daily life, you may come across problems like arranging people with given the number seats, arranging digits on place, arranging the numbers or alphabets, etc. You can list all the possible arrangements to count the total number of possible arrangements. If the total number of possible arrangements are too high, it won't be possible to list all the arrangements. Therefore you need some counting techniques to answer such questions without listing all the arrangements. In NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.1, you will learn the fundamental principle of counting which is used in all these techniques. You will find the most of the questions in NCERT book Class 11 Maths Chapter 7 Exercise 7.1 are related to the fundamental principle of counting only.

The 11th class maths exercise 7.1 answers have been meticulously prepared by highly qualified subject experts at Careers360. These Solutions are presented in great detail, explaining each step of the problem-solving process. Additionally, PDF versions of the ex 7.1 class 11 solutions are provided for students to download and use free of charge, making it a valuable resource for their studies. You can click on the NCERT solutions link where you will get detailed solutions from Class 6 to Class 12 at one place.

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**As per the CBSE Syllabus for 2023-24, this chapter has been renumbered as Chapter 6.

## Question:1(i) How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed?

The five digits are 1, 2, 3, 4 and 5

As we know that repetition of the digits is allowed,

so, the unit place can be filled by any of five digits.

Similarly, tens and hundreds of digits can also be filled by any of the five digits.

$\therefore$ A number of 3-digit numbers can be formed $=5\times 5\times 5=125$

The five digits are 1, 2, 3, 4 and 5

As we know that repetition of the digits is not allowed,

so, the unit place can be filled by any of five digits.

Tens place can be filled with any of the remaining four digits.

Hundreds place can be filled with any of the remaining three digits.

$\therefore$ Number of 3-digit numbers can be formed when repetition is not allowed $=5\times 4\times 3=60$

The six digits are 1, 2, 3, 4 ,5 and 6

As we know that repetition of the digits is allowed,

so, the unit place can be filled by any of even digits i.e.2,4 or 6

Similarly, tens and hundreds of digits can also be filled by any of six digits.

$\therefore$ Number of 3-digit even numbers can be formed $=3\times 6\times 6=108$

There are 10 letters of English alphabets.

As we know that repetition of the letters is not allowed,

so, the first place can be filled by any of 10 letters.

Second place can be filled with any of the remaining 9 letters.

Third place can be filled with any of the remaining 8 letters.

The fourth place can be filled with any of the remaining 7 letters.

$\therefore$ Number of 4-letter code can be formed when the repetition of letters is not allowed $=10\times 9\times 8\times 7=5040$

Hence, 5040 4-letter codes can be formed using the first 10 letters of the English alphabet, if no letter can be repeated.

First, two digits among 5-digit telephone numbers are fixed and rest 3 digits are variable.

$6,7,-,-,-$

The 10 digits are from 0 to 9.

As we know that repetition of the digits is not allowed,

so, the first and second place is filled by two digits 67

Third place can be filled with any of the remaining 8 digits.

The fourth place can be filled with any of the remaining 7 digits.

The fifth place can be filled with any of the remaining 6 digits.

$\therefore$ Number of 5-digit telephone numbers can be formed when repetition is not allowed $=8\times 7\times 6=336$

When a coin is tossed the number of outcomes is 2 i.e. head or tail.

When a coin is tossed 3 times then by multiplication principle,

the number of outcomes $=2\times 2\times 2=8$

Each signal requires use of 2 flags.

There will be as many flags as there are ways of filling in 2 vacant places in succession by the given 5 flags of different colours.

The upper vacant place can be filled in 5 different ways with any of 5 flags and lower vacant place can be filled in 4 different ways by any of rest 4 flags.

Hence, by multiplication principle number of different signals that can be generated $=5\times 4=20$

## More About NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.1:-

Class 11 Maths chapter 7 exercise 7.1 consists of questions related to finding the total number of possible arrangements of an event. Exercise 7.1 Class 11 Maths is based on the fundamental principle of counting. There are four examples given in the textbook before Class 11 Maths chapter 7 exercise 7.1 which are based on the counting principle only. You can go through these examples to get familiar with counting the possible arrangements. The permutations and combinations are new concepts added in the Class 11 Maths. So you may find it difficult to understand this chapter. Class 11 Maths chapter 7 exercise 7.1 solutions are here to help you to understand the concept easily.

## Benefits of NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.1:-

• Exercise 7.1 Class 11 Maths is a basic exercise that will help you understand this chapter very easily.
• You are advised to solve all the NCERT syllabus problems of Class 11 Maths Chapter 7 Exercise 7.1 by yourself.
• The upcoming exercises of this chapter are based on the fundamental of the principle of counting which you will learn in the Class 11 Maths chapter 7 exercise 7.1 solutions.
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## Key Features of NCERT 11th Class Maths Exercise 7.1 Answers

1. Thorough Coverage: The ex 7.1 class 11 answers encompass all the exercises and problems presented in Chapter 7.1 of the NCERT 11th Class Mathematics textbook.

2. Step-by-Step Guidance: The class 11 maths ex 7.1 solutions are meticulously structured with step-by-step explanations, facilitating easy comprehension for students.

3. Precision and Clarity: The class 11 ex 7.1 answers are drafted with precision and clarity to ensure students can grasp the mathematical concepts and problem-solving methods.

4. Free Access: These class 11 maths chapter 7 exercise 7.1 solutions are typically accessible free of charge, making them a valuable resource for self-study.

5. Homework and Practice: Students can utilize these answers to verify their work, practice problem-solving, and enhance their overall mathematical proficiency.

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## Subject Wise NCERT Exampler Solutions

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1. How many 2 digit even numbers can be formed from the digits 3, 4, 5 if the digits can be repeated?

Total number of arrangements = 3 x 1 = 3

There are only three ways to form 2 digit even number with the given condition.

2. How many 2 digit even numbers can be formed from the digits 3, 4, 5 if the digits can't be repeated ?

Total number of arrangements = 2x 1 = 2

There are only two ways to form 2 digit even number with the given condition.

3. How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 6 if the digits can be repeated?

Total number of arrangements = 5 x 5 x 3 = 75

There are 75 ways to form 3 digit even number with the given condition.

4. How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 6 if the digits can't be repeated ?

Total number of arrangements = 3 x 4 x 3 = 36

There are 36 ways to form 3 digit even number with the given condition.

5. What is the weightage of the Permutations and combinations in the CBSE exam ?

The whole algebra part has 30 marks weightage in the CBSE Class 11 Maths exam.

6. What is the syllabus of CBSE Class 11 Maths ?

Here you will get detailed syllabus for  CBSE Class 11 Maths.

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