Question

A garage door code has 5 digits. If no digit is repeated, how many codes are possible?

Hint: the possible digits are 0-9

Answer 1

There are 30240 possible codes.

Explanation:

For the first digit, there are 10 number choices possible:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

For the second digit, 9 number choices, because one of the digits cannot be repeated.

For the third, 8 number choices, because two of the digits cannot be repeated.

For the fourth, 7 number choices, because three of the digits cannot be repeated.

For the fifth, 6 number choices because four of the digits cannot be repeated.

Now multiply all the numbers, and you can see that there are 10*9*8*7*6, or 30240 codes possible.