Combinations of locks

Question

A company produces combination of locks, the combination consists of three numbers from 0 to 39 inclusive. Because of the construction no number can occur twice in a combination how many different locks can be attained?

Answer 1

There are $40$ possible numbers $(00-39)$ for the first digit of the combination. Because we cannot use the first digit again, we now have $39$ possible numbers for the second digit. We cannot use the first two digits for the third digit of the lock, so we now have $38$ possible numbers to choose from the digit. This gives us $(40 \cdot 39 \cdot 38)=59280$ possible combinations.