How many different license plates could be made if they have one or two letters followed by 1,2,or 3 digits? Reptetitions are allowed.
I figured that 26 would be for 1 letter and 52 for 2 letters
so (26+52) but not sure how to figure the numbers part.
26*10+26*10^2+26*10^3+
26^2*10+26^2*100 + 26^2*1000
check that.
To calculate the number of different license plates that could be made with one or two letters followed by 1, 2, or 3 digits, we need to consider each component separately.
For the letters:
- If one letter is allowed, there are 26 options (A-Z).
- If two letters are allowed, there are 26 options for the first letter and 26 options for the second letter. In total, there would be 26 x 26 = 676 possible combinations.
For the digits:
- If one digit is allowed, there are 10 options (0-9).
- If two digits are allowed, there are 10 options for the first digit and 10 options for the second digit. In total, there would be 10 x 10 = 100 possible combinations.
- If three digits are allowed, there are 10 options for each digit. In total, there would be 10 x 10 x 10 = 1000 possible combinations.
Since repetitions are allowed for both the letters and the digits, we need to add up the possibilities for each component.
- For one letter and one digit: 26 x 10 = 260 combinations.
- For one letter and two digits: 26 x 100 = 2600 combinations.
- For one letter and three digits: 26 x 1000 = 26000 combinations.
- For two letters and one digit: 676 x 10 = 6760 combinations.
- For two letters and two digits: 676 x 100 = 67600 combinations.
- For two letters and three digits: 676 x 1000 = 676000 combinations.
Finally, we sum up all the possibilities:
260 + 2600 + 26000 + 6760 + 67600 + 676000 = 781220
Therefore, there could be 781,220 different license plates that could be made with one or two letters followed by 1, 2, or 3 digits.