Question

How many natural numbers smaller than ${10}^4$ are there, in the decimal notation of which all the digits. are different?

Answer 1

Natural numbers which are different and less than ${10}^4$.

So, range is from $1to999$.

One digit number from $1to9$

Considering single digit as $9$.

2 digit number as $9\times 9$.

3 digit number as $9\times 8\times 9$.

$9+9\times 9+9\times 8\times 9$

$=9(1+9+72)$

$=9\times 82$

$=738$