## Formation of the **biggest and smallest numbers**

For formation of **biggest** and **smallest** **numbers** from the given digits, first we should form all the possible numbers. After it we should find the **biggest** and **smallest number**. For this, we shall take an example.

### Example 1

If 4 digits 4, 8, 5, 7 are given and we have to form biggest and smallest number of 4 digits. Now, we can form twenty four four-digit numbers by using each of these digits only once.

Have a look-

From the above digits, we can form the numbers-

4857, 4578, 4758, 4875, 4587, 4785,

5487, 5478, 5847, 5874, 5748, 5784,

7485, 7458, 7845, 7854, 7548, 7584,

8457, 8475, 8574, 8547, 8745, 8754.

We should keep in mind that to form the **smallest number-**

- We should write smallest digit first and then remaining digits in ascending order. i.e. the
**smallest number**will be 4578.

To form the **biggest number-**

- We should write largest digit first and then remaining digits in descending order so the
**biggest number**from above numbers will be 8754.

### Formation of five digit number by using four digits

Now, if we have four digits and we have to use those four digits to form the smallest and biggest five digit numbers, we should keep in mind that to form the smallest number-

- We should write the
**smallest**digit twice and remaining digits in ascending order.

If we have to form **smallest** **five digit** number by using above four digits,

so the **smallest number** will be **44578**.

- Similarly to form the
**biggest**five digit number, we should write the**biggest**digit twice and remaining digits in descending order.

If we have to form **biggest five digit** number by using above four digits,

the **biggest five digit** number will be **88754**.

### Example 2

We shall take another example. In this example, we have three digits to form three digit smallest and biggest number.

We can form six numbers by using three digits only once and out of those we have to find the smallest and biggest number. Let’s have a look-

Digits are 9, 2 and 6. Now first we shall form all the possible the numbers. and those are-

269, 296, 629, 692, 926 and 962

- The smallest number is 269
- Biggest number is 962

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