Question

A social media account password includes a number from 0 to 9, an uppercase letter, a lowercase letter, and a special character, in that order.

a. There are 223,080 password combinations. How many special characters are there?

b.What is the probability of guessing the account password if you know the number and uppercase letter, but forget the rest? Express your answer as a fraction in the simplest form.
The probability is _____
.

Answer 1

A. There are 33 special characters.

B. The probability of guessing the password under the given circumstances is 1 out of 858 combinations.

Step-by-step explanation:

Step 1; First we need to determine all the possible values that can come in each space of the password.

From 0 to 9, there are a total of 10 values.

For uppercase letters, there are a total of 26 values from A, B, C, D ...Z

For lower case letters, there are also a total of 26 values from a, b, c, d ...z.

So out of these three characters, we have a total of 10 × 26 × 26 = 6,760 different combinations.

If there are 223,080 password combinations we need to divide this by 6,760 to calculate the possible values of the special characters.

6,760 × Number of possible special characters = 223,080,

Number of special characters = $\frac{223,080}{6,760}$ = 33. So there are 33 special characters.

Step 2; If the number and uppercase values are known then the  various lowercase letters and special characters are the unknown values.

The number of possible combinations = number of lowercase letters × number of special characters = 26 × 33 = 858.

So the probability of guessing the password is 1 out of 858 combinations.