There are 5 digits: 1,3,4,7,9. How many positive integers less than 600 can be formed using these 5 digits:
(a) if digits can be repeated.
There are 5 1-digit numbers.
There are 5*5 or 25 2-digit numbers.
There are 3*5*5 or 75 3-digit numbers. (we can only choose the
first digit as 1,3, or 4 (three ways) for the number to be less that 600.
That's 5+25+75 = 105 ways.
(b) if digits cannot be repeated.
There are 5 1-digit numbers.
There are 5*4 or 20 2-digit numbers.
There are 3*4*3 or 36 3-digit numbers. (we can only choose the
first digit as 1,3, or 4 (three ways) for the number to be less that 600.
That's 5+20+36=61 ways.
Edwin