# NCERT solutions for Class 11 Mathematics Textbook chapter 7 - Permutations and Combinations [Latest edition]

#### Chapters ## Chapter 7: Permutations and Combinations

[Page 138]

### NCERT solutions for Class 11 Mathematics Textbook Chapter 7 Permutations and Combinations [Page 138]

Q 1 | Page 138

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?

Q 1.2 | Page 138

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed?

Q 2 | Page 138

How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

Q 3 | Page 138

How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeat

Q 4 | Page 138

How many 5–digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

Q 5 | Page 138

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

Q 6 | Page 138

Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

[Pages 140 - 141]

### NCERT solutions for Class 11 Mathematics Textbook Chapter 7 Permutations and Combinations [Pages 140 - 141]

Q 1.1 | Page 140

Evaluate 8!

Q 1.2 | Page 140

Evaluate 4! – 3!

Q 2 | Page 141

Is 3! + 4! = 7!?

Q 3 | Page 141

Compute (8!)/(6! xx 2!)

Q 4 | Page 141

if 1/(6!) + 1/(7!) = x/(8!), find x

Q 5 | Page 141

Evaluate (n!)/((n-r)!) when  n = 6, r = 2

Q 5.1 | Page 141

Evaluate (n!)/((n-r)!) when  n = 6, r = 2

Q 5.2 | Page 141

Evaluate (n!)/((n-r)!), when n = 9, r = 5

[Page 148]

### NCERT solutions for Class 11 Mathematics Textbook Chapter 7 Permutations and Combinations [Page 148]

Q 1 | Page 148

How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

Q 2 | Page 148

How many 4-digit numbers are there with no digit repeated?

Q 3 | Page 148

How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?

Q 4 | Page 148

Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?

Q 5 | Page 148

From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?

Q 6 | Page 148

Find n if n – 1P3 : nP4 = 1 : 9

Q 7.1 | Page 148

Find r if ""^5P_r = 2^6 P_(r-1)

Q 7.1 | Page 148

Find r if ""^5P_r = 2^6 P_(r-1)

Q 7.2 | Page 148

Find r if ""^5P_r = ""^6P_(r-1)

Q 8 | Page 148

How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?

Q 9 | Page 148

How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if

(i) 4 letters are used at a time,

(ii) all letters are used at a time,

(iii) all letters are used but first letter is a vowel?

Q 10 | Page 148

In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?

Q 11.1 | Page 148

In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S

Q 11.2 | Page 148

In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together

Q 11.3 | Page 148

In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?

[Page 153]

### NCERT solutions for Class 11 Mathematics Textbook Chapter 7 Permutations and Combinations [Page 153]

Q 1 | Page 153

If nC8 = nC2, find nC2.

Q 2.1 | Page 153

Determine n if  ""^(2n)C_3 : ""^nC_3 = 12 : 1

Q 2.2 | Page 153

Determine n if  ""^(2n)C_3 : ""^nC_3 = 11: 1

Q 3 | Page 153

How many chords can be drawn through 21 points on a circle?

Q 4 | Page 153

In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?

Q 5 | Page 153

Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

Q 6 | Page 153

Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.

Q 7 | Page 153

In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

Q 8 | Page 153

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

Q 9 | Page 153

In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

[Pages 156 - 157]

### NCERT solutions for Class 11 Mathematics Textbook Chapter 7 Permutations and Combinations [Pages 156 - 157]

Q 1 | Page 156

How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?

Q 2 | Page 156

How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?

Q 3 | Page 156

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:

(i) exactly 3 girls?

(ii) atleast 3 girls?

(iii) atmost 3 girls?

Q 4 | Page 156

If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?

Q 5 | Page 157

How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?

Q 6 | Page 157

The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?

Q 7 | Page 157

In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?

Q 8 | Page 157

Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

Q 9 | Page 157

It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

Q 10 | Page 157

From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

Q 11 | Page 157

In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?

## Chapter 7: Permutations and Combinations ## NCERT solutions for Class 11 Mathematics Textbook chapter 7 - Permutations and Combinations

NCERT solutions for Class 11 Mathematics Textbook chapter 7 (Permutations and Combinations) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics Textbook solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 11 Mathematics Textbook chapter 7 Permutations and Combinations are Concept of Combinations, Fundamental Principle of Counting, Concept of Permutations, Introduction of Permutations and Combinations, Permutation Formula to Rescue and Type of Permutation, Smaller Set from Bigger Set, Derivation of Formulae and Their Connections, Simple Applications of Permutations and Combinations, Factorial N (N!) Permutations and Combinations.

Using NCERT Class 11 solutions Permutations and Combinations exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer NCERT Textbook Solutions to score more in exam.

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