Question

A state's license plates consist of four letters followed by three numerals, and 242 letter arrangements are not allowed. How many plates can the state issue?

Answer 1

Find all possible letter arrangements and since you know 242 are not allowed you can subtract that from your total and then find all numeral arrangements and add them onto your new total. This deals with a combination and permutation and that you should be able to use if you've learned it.

Answer 2

I'm still confused

Answer 3

You are dealing with a combination and so you must remember to use the formula you were taught for combinations and from there find the combination of possible numbers for the 3 and find all the combination of letters for the 4 while subtracting the 242 letter arrangements from the total number of letters you find using the combination technique

Answer 4

Do you happen to know if order matters?

Answer 5

no

Answer 6

no i dont

Answer 7

If not we will assume it does not and continue, if order does not matter you will have to count the available letters in the alphabet that you can use and how many each time, which is given as only 4 slots, and from that you must subtract 242 which are not allowed.

Answer 8

if it is a license plate the order matters

Answer 9

From the numbers you must do the same, find the available numbers for example, 0 through 9, and how many of those numbers you can use, which is given as 3. Using the formula for permutations without repetition ,
\[n^r\]
Where
n = number of things to choose from
r = how many of them we choose

And from that we can find our values and add them up.

Answer 10

Again, that is if order does not matter.