Question

In how many ways can 22 books on english and 20 books on hindi be placed in a row on a shelf so that two books on hindi may not be together?

Answer 1

one English book should be placed after every hindi book. 2 books of English, 1 book of hindi and book of English over one book of hindi.

Answer 2

Answer:

Required number of ways are 1771 ways.

Step-by-step explanation:

Given 22 books of English and 20 books of Hindi. We have to find the number of ways can 22 books on English and 20 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together.

In order to find the number of ways so that the no two Hindi books placed together we must place a English book between every two Hindi books.

H  E  H  E  H  E  H  E  H  E....H  E  H

where E denotes position of English and H denotes position of Hindi.

Since there are 22 books on English the number of places marked H are 23

Now, 20 books out of 23 can be chosen in $_{23}^{20}\textrm{C}$=$_{23}^{3}\textrm{C}$=   $\frac{23!}{20!3!}=\frac{23\times 22 \times 21}{3\times 2}=1771$

Hence, required number of ways are 1771 ways.