How many integers between 0 and 999 (up to 3 digits) contain only the digits 0,1,4,6,7 and 8?

Dear student

Since the condiction of non repeating numbers is not mentioned

we will assume repeating case as valid

Let the first number be 1

1,_,_

6 ways of filling second digit

and 6 ways of filling 3^rddigit

ie 36 ways

similary first number can be chosen in 5 ways

so total numbers 5 * 36 =180

Regards