A password consists of 3 letters followed by 2 digits. How many different passwords can be formed if letters can be repeated but digits cannot? (2000)
Practice Questions
1 question
Q1
A password consists of 3 letters followed by 2 digits. How many different passwords can be formed if letters can be repeated but digits cannot? (2000)
17576
15600
13000
12000
There are 26 choices for each letter (3 letters) and 10 choices for the first digit and 9 for the second. Total = 26^3 * 10 * 9 = 17576.
Questions & Step-by-step Solutions
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Q
Q: A password consists of 3 letters followed by 2 digits. How many different passwords can be formed if letters can be repeated but digits cannot? (2000)
Solution: There are 26 choices for each letter (3 letters) and 10 choices for the first digit and 9 for the second. Total = 26^3 * 10 * 9 = 17576.
Steps: 9
Step 1: Identify the components of the password. It consists of 3 letters followed by 2 digits.
Step 2: Determine how many choices there are for each letter. There are 26 letters in the English alphabet.
Step 3: Since letters can be repeated, for each of the 3 letters, you have 26 choices. So, for 3 letters, the total choices are 26 * 26 * 26, which is 26^3.
Step 4: Calculate 26^3. This equals 17576.
Step 5: Now, look at the digits. The first digit can be any of the 10 digits (0-9), so there are 10 choices for the first digit.
Step 6: For the second digit, since digits cannot be repeated, you have 9 choices left (one digit has already been used).
Step 7: Multiply the number of choices for the letters and the digits together. This gives you 26^3 (for letters) multiplied by 10 (for the first digit) multiplied by 9 (for the second digit).
Step 8: The final calculation is 17576 (from letters) * 10 (first digit) * 9 (second digit).
Step 9: Calculate the final total: 17576 * 10 * 9 = 1581840.
