Question

california license plates have the format ISAM123. How many different license plates are possible?

Answer 1

Let's look at the word ISAM123, and we see that it has 4 letters and 3 numbers.

By seeing this example we assume that repetition is not allowed.

We have 4 places to be filled with 26 letters and 3 places to be filled with 10 numbers.

_ × _ × _ × _ × _×_× _ total 7 places

So let's fill this,

First place can have any letter out of 26, 2nd place can have any letter excluding the letter on the 1st place, similarly 3rd can have any but excluding 1st and 2nd place letters, and same for 4th place.

So, now 5th place can have any number out of 10 (0-9) and 6th place can have any number excluding number on the 5th place, same for 7th place.

Summing up all is equals to

26 × 25 × 24 × 23 × 10× 9 × 8 = 258,336,000 possible plates