NCERT Solutions Class 11 Mathematics Chapter 7 Permutations And Combinationsm Download In Pdf

Chapter 7 Permutations And Combinations Download in pdf

** Question 1.**How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5
assuming that

(i) repetition of the digits is allowed?

(ii) repetition of the digits is not allowed?

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

** Question 3.**How many 4-letter code can be formed using the first 10 letters of the English
alphabet, if no letter can be repeated?

** Question 4.**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?

** Question 5.**A coin is tossed 3 times and the outcomes are recorded. How many possible
outcomes are there?

** Question 6.**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?

** Question 1.**Evaluate

(i) 8 !

(ii) 4 ! – 3 !

** Question 2.**Is 3 ! + 4 ! = 7 ! ?

** Question 3.**Compute
8!
6!× 2!

** Question 4.**If
1 1
6! 7! 8!
+ = x , find x

** Question 5.**Evaluate ( )
!
!
n
n − r , when

(i) n = 6, r = 2

(ii) n = 9, r = 5.

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

** Question 2.**How many 4-digit numbers are there with no digit repeated?

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

** Question 4.**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?

** Question 5.**From a committee of 8 persons, in how many ways can we choose a chairman
and a vice chairman assuming one person can not hold more than one position?

** Question 6.**Find n if n – 1P3 : nP4 = 1 : 9.

** Question 7.**Find r if

(i) 5 6
Pr 2 Pr−1 =

(ii) 5 6
Pr Pr−1 = .

** Question 8.**How many words, with or without meaning, can be formed using all the letters of
the word EQUATION, using each letter exactly once?

** Question 9.**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?

** Question 10.**In how many of the distinct permutations of the letters in MISSISSIPPI do the
four I’s not come together?

**Question 11.**In how many ways can the letters of the word PERMUTATIONS be arranged if the
(i) words start with P and end with S, (ii) vowels are all together,
(iii) there are always 4 letters between P and S?

EXERCISE 7.4

** Question 1.**If nC8 = nC2, find nC 2.

**
Question 2.**Determine n if
(i) 2nC2 : nC2 = 12 : 1 (ii) 2nC3 : nC3 = 11 : 1

** Question 3.**How many chords can be drawn through 21 points on a circle?

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

** Question 5.**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.

** Question 6.**Determine the number of 5 card combinations out of a deck of 52 cards if there
is exactly one ace in each combination.

** Question 7.**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?

** Question 8.**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.

** Question 9.**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?

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- Chapter 1 Sets
- chapter 2 Relations And Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutations And Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences And Series
- Chapter 10 Straight Lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction To Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability

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