**What is Permutation?**

The different arrangements which can be made out of a given number of things by taking some or all at a time are called permutations.

**Examples:**

**1)** What are the two digit numbers that can be formed using the digits $2, 5, 7$.

**Solution: **

Here out of three digits, we formed two digit numbers, (i.e) we form numbers by taking two digits at a time.

The numbers that can be formed are, $25, 27, 52, 57, 72, 75$.

**2)** What are the different numbers that can be formed using all the digits, $9, 8$ and $5$.

**Solution: **

Here we form numbers by taking all at a time. (i. e) we form three digit numbers by taking all the digits at a time.

The numbers that can be formed are $589, 598, 859, 895, 958$ and $985$

**NOTE: Hence we observe that in permutations there will be selection and then arrangements.**

**What is Combination?**

Each of the different groups or selections which can be formed by taking some or all of a number of objects irrespective of their arrangements, is called a combination.

**Example:**

**1)** John as three pens each of blue, red and green. In how many ways two pens can be selected from the three pens.

**Solution:**

John as three colored pens each of blue, red and green.

The different ways of selecting two pens are, blue and red ; red and green (or) blue and green.

Therefore there are three ways of selecting two pens from three pens.

**2)** A bag has an yellow marble, black marble and a blue marble. In how many ways three marbles can be selected?

**Solution:**

Since the bag contains three marbles each of yellow, black and blue, the selection of thee marbles contain all the three colors yellow, black and blue.

Therefore, the selection can be done only one way.

**NOTE: Hence we observe that in combinations there will be only selection (and no arrangement).**