sachindia wrote:There are 5 chairs. Bob and Rachel want to sit such that Bob is always left to Rachel. How many ways it can be
done?

Here's one more approach.

Select any 2 chairs out of the 5 chairs.
Since the order of the selected chairs does not matter, we can use combinations.
We can select 2 chairs in 5C2 ways (10 ways)

At this point we're done. These 2 chairs are for Bob and Rachel, and if Bob must sit to the left of Rachel, there's only one way for them to occupy these 2 chairs.

Answer = 10

Aside: If anyone is interested, we have a free video on calculating combinations (like 5C2) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

Cheers,
Brent

Here's another way to look at it.

Take the task of seating Bob and Rachel and break it into stages.

Stage 1: Select two chairs
The order of the two selected chairs doesn't matter. For example, selecting chair #3 then chair #5 is the same as selecting chair #5 then chair #3
So, we can use combinations.
We can select 2 chairs in 5C2 ways (10 ways)

Stage 2: Seat Bob and Rachel in the two chairs
Since Bob must sit to the left of Rachel, there's only 1 way for them to occupy these 2 chairs.
In other words, there's only 1 way to accomplish stage 2

By the Fundamental Counting Principle (FCP) we can complete the two stages (and thus seat Bob and Rachel) in (10)(1) ways ([spoiler]= 10 ways[/spoiler])

Does that help clarify things?

Cheers,
Brent

Aside: For more information about the FCP, we have a free video on the subject: https://www.gmatprepnow.com/module/gmat-counting?id=775