ICM license plates

[Ruby_Salamone]

License plates in a certain state must have 4 letters (not I or O) followed by 3 digits. The last digit cannot be zero. How many license plates are possible?

 

[JeffM]

How many letters can you select from.

How many ways can you select the first letter?

How many ways can you select the second letter?

How many ways can you select the third letter?

How many ways can you select the fourth letter?

How many digits can you select from?

How many ways can you select the first digit?

How many ways can you select the second digit?

How many ways can you select the third digit?

So what is the answer?

 

[Ruby_Salamone]

would it be 24^4 times 10^3? which equals 331776000

 

[JeffM]

Not quite. You can select the first digit 10 ways, and the second digit 10 ways, but you can omly select the third digit 9 ways.

So the correct answer is [MATH]24^4 * 10^2 * 9 = 900 * 24^4.[/MATH]
This kind of problem is not really hard, but it usually requires very careful attention to detail.

 

[Ruby_Salamone]

Thanks!