Question

There are $10$ different books in a shelf. Find the number of ways in which $3$ books can be selected so that exactly two of them are consecutive.

Answer 1

$10$ books in a shelf

Select $3$ books such that exactly two are

Consecutive Total possibilities Total possibilities(Trends)

Number of ways $=6\times 7+7\times 2=56$

No.of books No of books

from which from which

$3^{rd}$ book $3^{rd}$ book

is selected is selected

when other two when other two

books are in books are in

middle either end