COUNTING TECHNIQUES

Let me begin by asking a simple question:

Say, if you have 5 shirts and 6 T-shirts, then in how many ways can you wear them to college without wearing one again? 11 ways, isn�t it ??

But if I say, if you have 5 shirts and 6 pairs of trousers, then in how many ways can you wear them to college without wearing one again. It isn�t that simple!! Or is it??

Here, for any shirt selected to wear, you can wear any one of the 6 trousers.
This means:
With say Shirt S-1, you can wear trouser T-1 or T-2 or T-3 or T-4 or T-5 or T-6 i.e. 6 ways. Similarly with Shirt S-2, you can wear trouser T-1 or T-2 or T-3 or T-4 or T-5 or T-6 i.e. 6 ways again.
&
so on till you do the same with the last shirt i.e.Shirt-5

Hence, total number of ways are : 6+6+6+6+6 = 30 ways.

If you have understood the counting technique behind these simple problems, then it is time to understand the below formulae to save time.

This also means OR indicates ADDITION (This is also known as DISJOINT SUM RULE).

This also means AND indicates MULTIPLICATION (This is also known as PRODUCT RULE).

Try inventing problems on your own and count the number of ways you can a �particular� thing or �any� thing.

Happy Counting!