Question

How many different 3 digit numbers less than 500 can be made using the digits 3, 4, 5, and 6 if the digits can be used only once

Answer 1

Number of choices for the first digit = 4
Since there cannot be repetitions,
Number of choices for the second digit = 3
similarly,
Number of choices for the third digit = 2

By the multiplication principle, the number of different 3-digit numbers with distinct digits that can be made from 4
= 4*3*2 = ?

Answer 2

However, not all of those numbers are less than 500.

choices for 1st digit: 2 (3 or 4)
choices for 2nd digit: 3
choices for 3rd digit: 2

so, there are really only 12 possible numbers less than 500