In how many ways can 21 books on english and 19 books on hindi be placed in a row on a shelf so that two books on hindi may not be together??

No two Hindi books are together.

Hindi and English books have to be arranged in a row on a shelf.

Number of English books = 21

Number of Hindi books = 19

Hindi books can be placed in the gaps between the English books. (Total number of gaps when 21 English books are placed = 22, including the gaps on the exterior ends of the books)

Number of combinations that can be formed = 22 C 19

Now, because the order of books doesn’t matter, number of ways in which Hindi and English books can be placed= 19! (Hindi books) and 21! (English books)

So, total number of combinations that can be formed = 21! * 19! * 22 C 19