Question

A door has a 3 digit password where no digits are repeated. What is the probability of guessing the correct password if there is only way to open the door?

• A. $\frac{1}{720}$
• B. $\frac{1}{10}$
• C. $\frac{1}{80}$
• D. $\frac{1}{90}$

Answer 1

The correct option is A $\frac{1}{720}$

The password of the door is a 3 digit number.

First digit can be chosen from 0 through 9 in 10 different ways.

The second digit can be chosen from 0 through 9 excluding the digit in the first place already chosen in 9 different ways.

The third digit can be chosen from 0 through 9 excluding the digits in the first and second places already chosen in 8 different ways.

The total number of combinations are
$10\times 9\times 8$ = $720$

Only one time we can get the correct password.

Probability of getting the correct password is
$\text{P}=\frac{1}{10\times 9\times 8}=\frac{1}{720}$