CBSE (Commerce) Class 11CBSE
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NCERT solutions Mathematics Class 11 chapter 7 Permutations and Combinations

Chapters

NCERT Mathematics Class 11

Mathematics Textbook for Class 11

Chapter 7 - Permutations and Combinations

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 | 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 1.2 | 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 2 | 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 3 | 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 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 4 | Page 138

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

Q 5 | 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?

Q 6 | Page 138

Pages 140 - 141

Evaluate 8!

Q 1.1 | Page 140

Evaluate 4! – 3!

Q 1.2 | Page 140

Is 3! + 4! = 7!?

Q 2 | Page 141

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

Q 3 | Page 141

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

Q 4 | Page 141

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

Q 5 | Page 141

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

Q 5.1 | Page 141

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

Q 5.2 | Page 141

Page 148

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

Q 1 | Page 148

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

Q 2 | 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 3 | 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 4 | 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 5 | Page 148

Find n if n – 1P3 : nP4 = 1 : 9

Q 6 | 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 7.1 | Page 148

Find r if `""^5P_r = ""^6P_(r-1)`

Q 7.2 | 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 8 | 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 9 | Page 148

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

Q 10 | 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 11.1 | Page 148

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

Q 11.2 | 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?

 
Q 11.3 | Page 148

Page 153

If nC8 = nC2, find nC2.

Q 1 | Page 153

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

Q 2.1 | Page 153

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

Q 2.2 | Page 153

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

Q 3 | Page 153

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

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 4 | 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 5 | 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 6 | 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 7 | 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 8 | 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?

Q 9 | Page 153

Pages 156 - 157

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 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 1 | 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 2 | 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 3 | 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 4 | Page 156

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 5 | 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 6 | 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 7 | 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 8 | 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 9 | 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 10 | Page 157

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

Q 11 | Page 157

NCERT Mathematics Class 11

Mathematics Textbook for Class 11
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