Question

How many natural numbers less than can be formed from the digits when a digit may be repeated any number of times?

Medium
Solution
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There are one-digit natural numbers out of the given digits.

For getting natural numbers we cannot put at the ten's place. So, this place can be filled by any of the given five nonzero digits in ways.

The unit's digit can be filled by any of the given six digits in ways.
So, the number of natural numbers .

Similarly, to get a number, we cannot put on at the hundred's place. So, this place can be filled in ways, each of the ten's and unit's places can be filled in ways.

the number of numbers .

Required number of numbers .

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