Worked solution
Count a licence plate when symbols may repeat
How many different license plates are available if each plate contains a sequence of three letters followed by three digits given that the letters and digits may be repeated?
CJC · Lecture · Example 5
Fill all six positions using their own choice counts
Use six ordered boxes, three for letters followed by three for digits.
| Position | Letter 1 | Letter 2 | Letter 3 | Digit 1 | Digit 2 | Digit 3 |
|---|---|---|---|---|---|---|
| Choices | 26 | 26 | 26 | 10 | 10 | 10 |
Repetition means the available count does not decrease after choosing a symbol.
How did this part go?
Multiply the six counts
Total number=. This uses the source model of 26 letters and 10 digits with no additional plate restrictions; the digit section may start with 0.
How did this part go?
Common mistakes
Repetition leaves the next position’s choices unchanged. Do not use decreasing factors such as 26×25×24 unless repetition is forbidden.