Question

J.K. Rowling buys 7 novels from a book fair, C.S. Lewis buys 8 jk. Rowling buy 7 novel from a book fair Cs lewis buy 8 novels from another book fair, none of which is in common with those bought by Rowling. They decide to exchange their books one for one. In how many ways can they exchange their books
for the first time?

Answer 1

They both can exchange their books one-by-one in 36 different ways.

According to the question,

JK Rowling bought 7 novels.

Lewis bought 8 novels.

They exchange their novels one-by-one.

The first novel of Rowling can be exchanged with any of the 8 novels of Lewis.

The second novel of Rowling can be exchanged with any of the remaining 7 novels of Lewis.

The third novel of Rowling can be exchanged with the remaining 6 novels of Lewis.

Similarly, the second novel of Rowling can be exchanged with the only remaining novel of Lewis.

Lewis will have one novel remaining.

So, the maximum possible ways of a two-way-exchange for the first time = 8+7+6+5+4+3+2+1 = 36.