Question

In how many ways the 18 english and 12 hindi books can be kept on the shelf so that two books on hindi may not be together.

Answer 1

Answer:

In mathematics, a combination is a method of picking elements from a set without regard to their sequence of selection. Let's say we have three numbers: P, Q, and R. Assortment determines how many ways we may choose two numbers from each group.

Given:

English books are $18$.

Hindi books are $12$.

To find:

We have to find the how many ways the books can be kept on the shelf so that two books on Hindi may not be together.

Solution:

Let E - Position of English book

Let H - Position of Hindi book.

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

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

Since there are $18$ books on English, we can choose $19$ places to place $12$ Hindi books.

$19C_{12}$

$=(19*18*17*16*15*14*13*12)/(6*5*4*3*2)\\=1540$

Final answer:

So the final answer of the question is $1540$ ways.

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