KC Sinha Mathematics Solution Class 11 Chapter 14 Permutations Exercise 14.1

 Exercise 14.1

Page no -14.10

Question 1

A movie theatre has 3 entrances and 4 exits. In how many ways can a man enter and exit from the theatre?

Question 2

There are 3 nominations for the post of president, 4 for the post of vice-president and 5 for the secretary.

(i) In how many ways can candidates be selected for each of these posts?

(ii) In how many ways can any one of these posts be filled?

Question 3

Find the number of possible outcomes of tossing a coin four times.

Question 4

(i) A class consists of 27 boys and 14 girls. In how many ways can one boy and one girl be selected to represent the class at a function ?

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

Question 5

Numbers 1, 2 and 3 are written on three cards. How many two digit numbers can be formed by placing two cards side by side ?

Question 6

A person wants to go to another city by bus and return by train. He has a choice of 5 different buses and 4 trains to return. In how many ways can he perform his journey ?

Question 7

Eight children are standing in a queue.

(i) In how many way can the queue be formed?

(ii) How many arrangements are possible if the tallest child stands at the end of the queue?

Question 8

In how many ways can a student answer a set of ten true/false type questions?

Question 9

How many numbers are there between 100 and 1000 in which all the digits are distinct ?

Question 10

There are seven flags of different Colour . A signal is generated using two flags. How many different signals can be generated?

Question 11

How many 3-digit numbers can be formed from the digits $1,2,3,4$ and 5 , if

(i) repetition of digits is allowed,

(ii) repetition of digits is not allowed.

Question 12

How many numbers can be formed from the digits $1,2,3$ and 9 , if repetition of digits is not allowed?

Question 13

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

Question 14

How many three digit number with distinct digits are there whose all the digits are odd?

Question 15

The first ten English alphabet are written on slips of paper and placed in a box. Three of the slips are drawn and placed in order. How many arrangements are possible? 

Question 16

How many 4-letter code can be formed using the first 10 letters of the English alphabet. If no letter can be repeated ? 

Page no 0 14.11

Question 17

How many 4-digit numbers greater than 2300 can be formed with the digits $0,1,2,3,4,5$ and 6 , no digit being repeated in any number?

Question 18

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

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

(iii) How many 5 -digit numbers can be formed using the digits $0,1,2,3$ and 4 , if the digits can be repeated in a number ?

Question 19

How many 3 -digit numbers have exactly one of their digits as 5 ?

Question 20

In how many ways can 3 people be seated in a row containing 7 seats? 

Question 21

A letter lock consists of three rings, each marked with 10 different letters. In how many ways is it possible to make an unsuccessful attempt to open the lock?

Question 22

How many five digit telephone numbers can be constructed using the digits 0 to 9 .

(i) If each number starts with 59 , for example 59612 etc., and no digit appears more than once ?

(ii) If each number starts with 67 and no digit appears more than once ?

Question 23

Find the number of ways in which one can post 4 letters in 6 letter boxes.

Question 24

In how many ways can 4 different balls be distributed among 5 boxes, when

(i) no box has more than one ball.

(ii) a box can have any number of balls.

(iii) no box contains all the balls.

Question 25

(i) 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 ?

(ii) Given 4 flags of different colours, how many different signals can be generated if a signal requires the use of 2 flags one below the other ?

(iii) Find the number of different signals that can be generated by arranging at least two flags in order (one below the other) on a vertical staff, if five different flags are available.

Question 26

Find the total number of ways in which $n$ distinct objects can be put into two different boxes.

Question 27

A telegraph has 5 arms and each arm can have three distinct positions. including the position of rest. How many signals can be made using the telegraph ?

Question 28

A team consists of 5 boys and 4 girls. It plays singles matches against another team consisting of 6 boys and 3 girls. How many matches can be arranged between the two teams if a boy plays against a boy and a girl plays against a girl?

Question 29

Rajeev has 3 pants and 2 shirts. How many different pairs of a pant and a shirt, can he dress up with ?

Question 30

Ali has 2 school bags, 3 tiffin boxes and 2 water bottles. In tow many ways can he carry these items choosing one each.