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FOrmINg NumberS

Without repetition of Digits

We can form many 3-digit numbers with the given digits. Let us form all the possible
numbers using the digits 1, 5 and 4.

H T O H T O H T O

1 5 4 5 4 1 4 1 5
1 4 5 5 1 4 4 5 1

1 in the hundreds place 5 in the hundreds place 4 in the hundreds place

Here, 541 is the greatest number and 145 is the smallest number formed with the
digits 1, 4 and 5. We see that the digits (1, 4 and 5) are in increasing order in the
smallest number 145 and in decreasing order in the greatest number 541.

greatest Number

To form the greatest number with the given digits, write the digits in decreasing order
(descending order).
TTh Th H T O
example 1. Form the greatest 5-digit number using the digits
6, 5, 0, 3 and 1. 6 5 3 1 0

Solution. We write the digits in descending order. greatest smallest
The greatest number formed with the given digits is 65,310. digit digit

Smallest Number

To form the smallest number with the given digits, write the digits in increasing order
(ascending order).

example 2. Form the smallest 5-digit number using the digits 5, 8, 4, 0 and 3.

Solution. To form the smallest number with 0 as one of the
given digits, we write 0 at the second place from the left TTh Th H T O
and then write the other digits in ascending order. 3 0 4 5 8
The smallest number formed with the given digits is 30,458.
second greatest
With repetition of Digits smallest digit digit

greatest Number

example 3. Form the greatest 5-digit number using the digits 5, TTh Th H T O
1, 4 and 6 by repeating the digits.
6 6 5 4 1
Solution. We repeat the greatest digit (6).
The greatest 5-digit number formed with the given digits is 66,541.

16 Mathematics 4