Question

the number of ways that 5 Mathematics 3 physics and 2 Chemistry books can be arranged so that the 3 Physics books kept together and the two chemistry books not together is

Answer 1

Say you take a cord and tie the physics books (so that they are always together )

*You can do this in 3! Ways*

Now you've got 5 math books, two Chem and one physics bundle

First arrange the math books and physics bundle

*You can do that in 6! ways*

After arranging 6 objects, you get 7 gaps

By arranging the Chem books in these gaps you make sure that they aren't together

2 books 7 gaps

*So you can arrange them in 7 C 2 ways*

So finally by the fundamental principle of multiplication, you get the no of ways as
=3!*6!*(7 C 2)