Permutation: Permutation means arrangement of things. The word arrangement is used, if the order of things is considered.

**ORDER IS IMPORTANT**

පිලිවෙලකට අනුව සැකසිය හැකි ආකාර

Combination: Combination means selection of things. The word selection is used, when the order of things has no importance.

**ORDER IS**

*NOT*IMPORTANTපිලිවෙලක් නැතුව තොරාගත හැකි ආකාර. පිලිවෙලක් නැති නිසා එකම පදය නැවත නැවතත් ලියනු නොලැබෙ.

The only things you need to remember are the formulas.

Permutation Formula:

^{n}P

_{r}= n! / (n - r)! Where r <= n

Read as, we have n items and want to pick k in a certain order.

Combination Formula:

^{n}C

_{r}= n! / ( r! x (n - r)! ) Where r <= n

Read as, we have n items and want to pick k number of items at a time.

If you are not familiar with n! (Factorial n), have a look at What is factorial?.

n! = 1 x 2 x 3 x ....... (n - 2) x (n - 1) x n

Though these might look quite strange, believe me these are very simple to use.

Let's take an example:

Say there are 5 letters, A B C D E. You are asked to pick 3 letters in order.

Here the n = 5 and k =3.

^{5}P

_{3}= 5! / (5 - 3)! = 5! / 2! = (5 x 4 x 3 x 2 x 1) / (2 x 1) = 5 x 4 x 3 = 60

So there are 60 ways to select 3 letters from a set of 5 letters in a particular order.

Here ABC and CAB are counted as 2 since the order is important.

If you are asked to pick 3 letters without considering the order (so that a combination) here is how we can do it.

^{5}C

_{3}= 5! / 3! x (5 - 3)! = (5 x 4 x 3 x 2 x 1) / (3 x 2 x 1) x (2 x 1) = 5 x 2 = 10

So there are 10 ways to select 3 letters from a set of 5 letters without an order.

Here ABC and CAB are counted as 1 since the order is NOT considered.

Note that we are talking about n items in a particular set here. If you were asked to chose items repeatedly on the same set, then you will need to multiply the result. For example, you are asked to select 1 letter from the set A and B. Then again asked to select 1 letter from A and B (Not considering that 1 is already select before). Finally the same process to chose 1 letter from A and B. So altogether we were asked 3 times to chose one letter each time on the same set then this is 3 combinations. Don't try to apply this on the same formula.

^{2}C

_{1}X

^{2}C

_{1}X

^{2}C

_{1}= 8

I guess you now have a simple idea on Permutations & Combinations now. Lets answer your posts now.