# Permutation of objects

#### Math Formulas

## Permutation of objects

**Definition :-**Permutation means the arrangement of taking some or all objects from the given objects.

**Description of formula :-**

Number of ways of arranging r distinct obejcts out of n distinct objects (repetition is allowed)

When repetition is not allowed.

Total ways = n(n – 1) (n -2) ……………. (n – r + 1)

**Real life example :-**

Suppose there is a party in your house of your son's birthday and you have invited 10 close friends in the party as you know that there is only 10 chairs in your house but the real problem occurs when you came to Know that your wife have gave 1 chair to your neighbour because some guests have visited on their home and they are short of 1 chair and your wife’ nature is very kind and helpful. So after know this you become tense as what will you do right now, So after thinking a lot you have decided that you will arrange 10 persons in 9 chairs by using the concept of permutation and you can arrange 10 persons in 9 chairs in 10P9 = 10 FACTORIAL OR 362880 WAYS.

So you can arrange 10 persons in 9 chairs in 362880 ways.

So this is just a basic real life application of permutation and likewise there numerous applications like arrange 4 employees of organization in 6 different chairs, arrange six different fruits in 5 trays.

**Example 1 :-**A code have 4 digits in a specific order, the digits are between 0-9. How many different permutations are there if one digit may only be used once?

**Solution :-**A four digit code could be anything between 0000 to 9999, hence there are 10,000 combinations if every digit could be used more than one time but since we are told in the question that one digit only may be used once it limits our number of combinations. In order to determine the correct number of permutations we simply plug in our values into our formula:

**Example 2 :-**A license plate begins with three letters. If the possible letters are A, B, C, D and E, how many different permutations of these letters can be made if no letter is used more than once?

**Solution :-
Using reasoning:**

For the first letter, there are 5 possible choices. After that letter is chosen, there are 4 possible choices. Finally, there are 3 possible choices.

5 × 4 × 3 = 60

**Using the permutation formula:**

The problem involves 5 things (A, B, C, D, E) taken 3 at a time.

There are 60 different permutations for the license plate.