Question

how many three digit numbers are possible with non repeating digit

Answer 1

Let us first select first digit. The first digit cannot be zero and hence it can be 1 of 9 digits: 1 to 9.
Once 1st digit is selected, for the second digit we can select 0 or any of the remaining 8 digits left after selecting the first digit
Hence second digit can be selected in 9 ways.
Third digit can be selected in 8 ways since we have selected 2 out of 10 digits..
Hence total number of possible non repeating 3 digit numbers = 9 x 9 x 8 = 648