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. What is the approximate probability that exactly one of the four characters will be a number? \( 1 \% \) \( 11 \% \) \( 28 \% \) \( 44 \% \)

To calculate the probability that exactly one of the four characters in the password is a number, we first identify how many lowercase letters (26) and digits (10) we have to work with. 1. Choose 1 position from 4 for the number: \( \binom{4}{1} = 4 \). 2. Choose 1 digit for that position: 10 ways. 3. Choose 3 lowercase letters from the 26 available letters without replacement. This is done as follows (since we are choosing distinct characters): - For the first letter, we have 26 options, 25 for the second, and 24 for the last letter: \( 26 \times 25 \times 24 \). 4. Combine these choices to find the total favorable outcomes: \( 4 \times 10 \times (26 \times 25 \times 24) \). 5. Total possible passwords without any restrictions are: \( 36 \times 35 \times 34 \times 33 \) (since there are 36 characters to choose from when considering lower case letters and digits together). Now the probability that exactly one character is a number is computed by dividing the total favorable outcomes by the total outcomes. When calculated, this approximately gives a result that leads us to the answer: So, \( \approx 11\% \). Thus, the answer is \( 11\% \).