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camila sets up a passcode on her smart phone, which allows only 7 digit codes. a spy sneaks a look at Camila’s phone and sees her fingerprints on the screen over seven numbers. what is the probability the spy is able to unlock the smart phone on his first try? express your answer as a fraction

Answer :

We have:

only 7 digit codes

The number of possible combinations is:

[tex]7i[/tex]

The probability the spy is able to unlock the smart phone on his first try is:

[tex]P=\frac{1}{7i}[/tex]

Then:

[tex]P=\frac{1}{7\times6\times5\times4\times3\times2\times1}=\frac{1}{5040}[/tex]

Answer:

[tex]\frac{1}{5040}[/tex]

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