1.  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?
A. 4586
B. 5896
C. 2415
D. 1771

Answer: Option D

Explanation:

In order that two books on Hindi are never together, we must place all these books as under:
H E H E H E H….. H E H

Where H denotes the position of Hindi book and E that of English book.

Since there are 22 books on English, the number of places marked E are 23.

Now, 20 places out of 23 can be chosen in 23C20

      = (23C3
= 23 x 22 x 21
3 x 2 x 1
= 1771.

Hence the number of ways = 1771 ways