Question

Outside a home, there is a 10-key keypad with the letters A, B, C, D, E, F, G, H, I, and J that can be used to open the garage if the correct ten-letter code is entered. Each key may only be used once. How many codes are possible? The number of possible codes is:_____

Answer 1

Answer:

3,628,800 (aka "10!")

Step-by-step explanation:

The first letter in the code can be 10 possible letters.

Since every letter can only be used once, the second letter can only be 9 possible letters.

E.G.: If the first letter is A, the second letter is B-J.

The third letter would be 8 possible letters, than the fourth would be 7, etc.

In math form, figuring out the possible combinations would be written out as so:

10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

An easier way to write this out would be using "10!", which stands for "10 Factorial"

The result of the above equals 3,628,800.