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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 :

Answer:

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:

[tex]\begin{gathered} n=10! \\ n=10\times9\times8\times7\times6\times5\times4\times3\times2\times1 \\ n=3,628,800 \end{gathered}[/tex]

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

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