Question

There are two friends Ram and Sandeep. Ram has x different physics books and Sandeep has y different mathematics books. Find the number of ways in which Ram and Sandeep can exchange their books in such a way that after exchanging they still have same number of books but not the same set.

• A. - 1
• B.
• C. - 1
• D. - 1

Answer 1

The correct option is D

- 1

Total number of books = x + y

Now let us keep all books at one place and ask Ram to pick x books out of these x + y books. He can do it in ${}^{x+y}{C}_x$ ways. Out of these ways there is one way when he picks those x books which he was initially having.

Thus the required numbers of ways are ${}^{x+y}{C}_x-1$.