Question

Outside a home there is a 10 key key pad with letters A B C D E F G H I and J that can be used to open a garage door If the correct 10 coded letter is entered. How many codes are possible?

Answer 1

Step-by-step explanation:

We were given the following:

The keypad is 10 key with letters A B C D E F G H I and J

Number of keys = 10

Number of code = 10

Each key may be used only once.

For the first code, 10 possible choices exist

For the second code, 9 possible choices exist

For the third code, 8 possible choices exist

For the fourth code, 7 possible choices exist

We will see the same trend till we get to the last code

The possibility of codes is calculated as shown below:

`\begin{gathered} n=10! \\ n=10*9*8*7*6*5*4*3*2*1 \\ n=3,628,800 \end{gathered}`

Therefore, the number of possible codes is 3,628,800