Question

A combination lock will open when the right choice of three numbers (from 1-40, inclusive) is selected. How many different lock combinations are possible?

Answer 1

`40xx39xx38=59,280`

Explanation:

If the three numbers need to be distinct:
then there are 40 choices for the first number;
then 39 choices for the second number (having eliminated one number);
then 38 choices for the third number (having eliminated two numbers).
`color(white)("XXX")40xx39xx38=59,280`

If the numbers do not have to be different:
there would be `40^3=64,000` combinations
(40 for each of the first, second and third choices).