Question

A password for a website must have 4 different digits. What is the probability a password chosen at random is 7654?

Answer 1

Answer:

0.02% probability a password chosen at random is 7654

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the numbers are chosen is important. For example, 7654 is a different password than 6754. So the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

What is the probability a password chosen at random is 7654?

Only one desired outcome(password 7654), so $D = 1$

Total outcomes:

4 numbers from a set of 10. So

$P_{(10,4)} = \frac{10!}{(10-4)!} = 5040$

Probability:

$p = \frac{D}{T} = \frac{1}{5040} = 0.0002$

0.02% probability a password chosen at random is 7654