Question

A randomly generated password contains four characters. Each of the four characters is either a lowercase letter or a digit from 0–9. Each character in the password cannot be used more than once.
HELP QUICKLY PLEASE
What is the approximate probability that exactly one of the four characters will be a number?

1%
11%
28%
44%

Answer 1

The correct answer is:

C. 28%

The approximate probability that exactly one of the four characters will be a number is 28%.

$|Huntrw6|$

Answer 2

Sample space is 36C4
Now, we want to know all of the combinations that have 1 digit in it.
So, we can have one here:

1XXX
X1XX
XX1X
XXX1

But we have 10 different digits to choose from. So, we need to introduce the combination term, nCr, where n is a list of all digits and r is how many we want.

Since we only want one, we will need 10C1 for the number of digits. But we need to choose three lowercases, so it becomes 10C1 × 26C3

Since it's a probability question, we need to divide that by our sample space, 36C4, and our percentage becomes 44%