Question

What will be the smallest 6-digit number that can be formed by the digits 9, 6, 0, 5, 8, 1 ?
A. 015,689
B. 1,05,689
C. 5,01,689
D. 9,86,510

Answer 1

Hint: As we know that in an n-digit number the first digit can never be 0, otherwise the number of digits will become equal to n – 1.

Complete step-by-step answer:
As we know that whenever we are asked with the smallest number then we place digits from left to right such that the leftmost digit is smallest and rightmost is the largest of all.
And if we are given n-different digits then we have to use all of them to form a n-digit smallest number. We cannot form a n-digit number by only using the smallest digit.
So, as we know that we are given six digits and that were 9, 6, 0, 5, 8, 1.
So, now we start placing all the digits from left to right.
To form a smallest number the first digit should be the smallest of the given digits (i.e. 0).
But if the first digit will be 0 then the number will become n–1 digit number.
So, the first digit will be the second smallest digit and the second digit off the number will be 0.
So, the first digit of the required number will be 1.
And the second digit of the required number will be 0.
Now there are 4-digits left and that was 9, 6, 5, 8.
So, the third digit will be the smallest of them (i.e. the third digit will be 5).
Fourth digit of the number will be 6.
Fifth digit of the number will be 8.
And the sixth digit of the number will be 9.
So, the smallest number that can be formed with the given 6-digits will be 1,05,689.
Hence, the required number will be B.

Note: Whenever we come up with this type of problem then first, we should remember 0 cannot be the first digit of the number so, 0 will be the second digit of the required number. And the first digit will be the next smaller digit that is greater than 0. And then we had to place digits such that digits increase from going left to right of the number.