Question

in how many ways can 20 books be arranged on the shelf so that a particular pair of books shall not come together​

Answer 1

Answer:

depends upon the shelf sise

ok.....

Step-by-step explanation:

Answer 2

Let’s say that the books are B1, B2, B3, … B20.

And let’s say that the particular pair that cannot be together are B1 and B2.

The easiest way to solve this is to compute the total number of ways to arrange these 20 books, and then subtract the number of ways that the books can be arranged where B1 and B2 are together.

The total number of ways to arrange these 20 books is 20!.

If B1 and B2 are together, think of them as one book. So there are now 19 books. The total number of ways to arrange these 19 books is 19!.

One last thing is that those two books can be in the order B1 B2 or B2 B1, so we must multiply this last value by 2 to get 2 x 19!.

Subtracting this from 20! gives 20! - (2 x 19!).