Consider the problem of distributing 10 distinct books among three different people with each person getting at least one book. Explain why the following solution strategy is wrong:

First select a book to give to the first person in 10 ways.

Second select a book to give to the second person in 9 ways.

Then select a book to give to the third person in 8 ways.

Finally distribute the remaining seven books in 7^3 ways.