A car license plate consists of 6 characters. The first 3 characters are letters excluding I, O, Q and U. The last 3 characters are any of the numerals 0 to 9 inclusive. How many different license plates are possible?
Please show your work.
Repetitions are permitted.
For the letters, there are 26-4=22 choices for each character.
For the numbers, there are 10 choices for each digit.
Total number of different licence plates
= 22^3*10^3
thank you so much. how come it wouldn't be 22P3*10P3?
When "Repetitions are permitted", you'd think of powers.
To find the number of different license plates that are possible, we need to calculate the number of options for each character and then multiply them together.
For the first character, there are 23 options (26 letters minus 3 excluded ones).
For the second character, there are also 23 options.
For the third character, again there are 23 options.
For the last three characters, which are numerals from 0 to 9 inclusive, each character has 10 options.
So, to find the total number of different license plates, we multiply the number of options for each character: 23 × 23 × 23 × 10 × 10 × 10 = 12,090,000.
Therefore, there are 12,090,000 different possible license plates.