Question

Find the number of natural numbers from $1$ to $1000$ having none of their digits repeated.

Answer 1

there can be 3 kind of numbers 1 digit 2 digit 3 digit no.s

No. of 1 digit no.s is 9 obviously.

No. of 2 digit no.s is $9\times 9=81$ as the 1st digit can't be 0 but the 2nd digit can

Similarly no. of 3 digit no.s = $9\times 9\times 8=648$

Total no. of no.s $=738$