# A lock has a dial with 50 numbers on it. To open it you must have a 3 digit code. How many possibilities are there if the 3 numbers must be different?

Jul 28, 2016

$50 \times 49 \times 48 = 117 , 600$

#### Explanation:

Break the process down into 3 steps:

For the first digit there are 50 values to choose from.
For the second digit there are now 49 values to choose from.
For the third digit there are now 48 values to choose from.

Each choice can be combined with each other choice.

$50 \times 49 \times 48 = 117 , 600$

There is also a formula you can use, but it is possible to think it out for yourself.

If the digits could be repeated, then the number of possibilities is
$50 \times 50 \times 50 = 125 , 000$