Permutation refers to the different ways of arranging a set of objects in a sequential order.

Combination refers to several ways of choosing items from a large set of objects, such that their order does not matters.

So, Permutations are for lists (order matters) and combinations are for groups (order does not matter).

Example: In a group of 6 boys and 4 girls, four children are to be selected such that 2 boys and 2 girls should be there.

Here, we have to select 2 boys from 6 boys and 2 girls from 4 girls and order does not matter.

So, we apply combination.

Now, total number of ways = ⁶C₂ * ⁴C₂

                                          = {(6*5)/(2*1)}*{(4*3)/(2*1)}

                                          = (30/2)*(12/2)

                                          = 15*6

                                         = 90 

Example: In how many different ways can the letters of the word LEADING be arranged such that the vowels should always come together?

When we arrange the letters, order is important. So we apply permutation here.

The word LEADING has 7 letters. It has the vowels E, A, I in it and these 3 vowels should always come together.

Hence these 3 vowels can be grouped and considered as a single letter. that is, LDNG(EAI).

Hence we can assume total letters as 5 and all these letters are different.

Number of ways to arrange these letters = 5! = 120

In the 3 vowels (EAI), all the vowels are different.

Number of ways to arrange these vowels among themselves = 3! = 6

Hence, required number of ways = 120*6 = 720