Question
A password consists of 3 letters of the alphabet followed by 3 digits chosen from 0 to 9. Repetition is allowed. How many different possible passwords are there? Your Answer: Answer
Ask by Robbins Campos. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There are 17,576,000 different possible passwords.
Solution
A password consists of 3 letters (with 26 choices each) and 3 digits (with 10 choices each). Since repetition is allowed, you simply multiply the number of possibilities for each position.
For the 3 letters: 26 × 26 × 26 = 26^3
For the 3 digits: 10 × 10 × 10 = 10^3
Thus, the total number of different passwords is 26^3 × 10^3 = 17,576,000.
Answer: 17,576,000.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To create a password consisting of 3 letters followed by 3 digits, we first calculate the number of options for each part. There are 26 letters in the alphabet, and for each of the 3 letters, we have 26 options. This gives us \(26^3\) combinations for the letters. For the digits, there are 10 options (0 to 9) for each of the 3 digits, resulting in \(10^3\) combinations for the digits. Therefore, the total number of different possible passwords is: \[ 26^3 \times 10^3 = 17576 \times 1000 = 17,576,000 \] So, there are a total of **17,576,000 different possible passwords**.
