Question

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

Answer 1

using permutations and combinations  and method of gaping
so there are 22 spaces between the 21 tamils books and there are 19 English books
 are identical  so it must be identified as  1 objest can be arrange there ²²P₁ = 22  ways

Answer 2

Answer:

Let T - Position of Tamil book

Let E - Position of English book.

In order to keep English books that are never together, we must place all these books as:

TETETETE....ETET

Since there are 21 books on TAMIL, we can choose 22 places to place 19 ENGLISH books.

22C19 = 22C3 = (22 x 21 x 20)/(3 x 2 x 1) = 1540 ways.