KC Sinha Mathematics Solution Class 11 Chapter 14 Permutations Exercise 14.4

 Exercise 14.4

Page no- 14.43

Type 4

Question 1

There are two books each of three volumes and two books each of two volumes. In how many ways can the ten books be arranged on a table so that the volumes of the same book are not separated.

Question 2

A library has 5 copies of one book, 4 copies of each of 2 books, 6 copies of each of 3 books and single copies of 8 books. In how many ways can all books be arranged so that copies of the same book are always together ?

Question 3

In a dinner party there are 10 Indians, 5 Americans and 5 Englishmen. In how many ways can they be seated in a row so that all persons of the same nationality sit together?

Page no- 14.43

Type 5

Question 4

In a class of students there are 4 girls and 6 boys . In how many ways can they be seated in a row so that all four girls are not together 

Question 5

Show that the number of ways in which $n$ books may be arranged on a shelf so that two particular books shall not be together is $(n-2)(n-1)$ !

Question 6

Six papers are set in an examination 2 of them in mathematics .In how many different orders can the papers be given if two mathematics papers are not successive? 

Question 7

You are given 6 balls of different colours (black, white, red, green, violet yellow), in how many ways can you arrange them in a row so that black and white balls may never come together ?

Question 8

In how many ways can 4 boys and 3 girls be seated in a row so that no two girls are together ?

Question 9

In how many ways can 15 I.Sc. and 12 B.Sc. candidates be arranged in a lint so that no two B.Sc. candidates may occupy consecutive positions?

Question 10

In how many ways can 18 white and 19 black balls be arranged in a row so that no two white balls may be together? It is given that balls of the same colour are identical.

Question 11

In how many ways can 16 rupees and 12 paise coins be arranged in a line so that no two paise coins may occupy consecutive positions?

Question 12

Show that the number of ways in which $p$ positive and $n$ negative signs may be placed in a row so that no two negative signs shall be together is $p+{ }^{1} C_{n}$.

Question 13

$m$ men and $n$ women are to be seated in a row so that no two women sit together, If $m>n$, then show that the number of ways in which they can be seated is $\frac{m !(m+1) !}{(m-n+1) !}$.

$[H O T S \mid$

Question 14

 women and 5 men are to sit in a row for a dinner. Find in how many ways they can be arranged so that no two women sit next to each other.

Question 15

Find the number of ways of arranging the letters $a, a, a, a, a$ $b, b, b, c, c, c, d, e, e, f$ in row, if letters $c$ are separated from one another.