How many liscence plates can Texas make? Details are below...?

Question

1)TEXAS MAKES PLATES WITH THREE # AND 4 LETTERS
2) YOU CAN USE # 0-9, AND ALL LETTERS EXCEPT I AND O.
3) IN ANOTHER SITUATION YOU CANNOT HAVE 0 FOR THE FIRST NUMBER.

HOW MANY PLATES CAN YOU MAKE IN BOTH SITUATIONS?
PLEASE TELL ME HOW YOU DID IT

Answer 1

Ok lets figure this spaces, first three are for numbers and next 4 for letters...

In first situation there are 10 possible numbers for each space and for the other spaces 24 letters...

10 x 10 x 10 x 24 x 24 x 24 x 24 = 331776000 possible plates

In second situation the first space has just 9 possibilities, so the answer would be:

9 x 10 x 10 x 24 x 24 x 24 x 24 = 298598400 possible plates

Answer 2

How many liscence plates can Texas make? Details are below...?
1)TEXAS MAKES PLATES WITH THREE # AND 4 LETTERS

Being from Texas, our plates are actually a maximum of six letters and numbers.

2) YOU CAN USE # 0-9, AND ALL LETTERS EXCEPT I AND O.

You did not specify if they needed to be in any particular sequence, or not. This leaves 10 numbers and 24 letters. So, 10^3 multiplied by 24^4 multiplied by 7. Why? Seven different spaces, 10 numbers in three places and 24 letters in 4 places.

Your answer is: 2,322,432,000 license plates.

If the plates do have to be in that specific order, then the answer is: 331,776,000.

3) IN ANOTHER SITUATION YOU CANNOT HAVE 0 FOR THE FIRST NUMBER.

This is almost the same as before.

IF you must keep the variable from above, then it would be: 9*10^2*24^4*7. Why. Only the first number can't be 0. That's why 9 instead of 10. The answer would be: 2,090,188,800.

IF NOT, then it would be 9*10^2*26^4*7. The answer would be: 12,203,544,080,000.


LASTLY, if the numbers and letters MUST STAY in the particular order they are given, then just leave off the multiplying by seven in both choices. You multiply by seven if you can have the numbers and letters in any order.

Answer 3

Let number of possible license plates = N

I am assuming that the first three digits are numbers followed by four letters. If numbers and letters can be mixed differently than that as well, the answer will be higher.

N = 9*10^2 * (26-2)^4
N = 9*10^2 * 24^4 = 298,598,400

Explanation:

The first digit is one of 9 possible (no zero)
The second and third digits are one of 10 possible
The last four digits are one of 24 possible

Answer 4

For all situation:
(# of digits available^# of spaces available for numbers) (# of letters that can be used^# of spaces available for letters) = # of possible combinations

For a situation that met the criteria of only 1:
(10^3) (26^4) = (1000) (456976) = 457,976,000 possible combinations

For a situation that met the criteria of 1 and 2:
(10^3) (24^4) = (1000) (331776) = 332,776,000 possible combinations

For a situation that met the criteria of 1 and 3:
(9^3) (26^4) = (729) (456976) = 333,135,504 possible combinations

For a situation that met the criteria of 1, 2 and 3:
(9^3) (24^4) = (729) (331776) = 241,864,704 possible combinations

Answer 5

there are 26 letters in the alphabet so for eact slot where there is only a letter there are 26 possibilities. Assuming that there are only 7 slots availiable and 3 slots with only letters thats 3^3 and 1 slot with a letter or number there are 26 + 10 possiblities, and 3 more slots with only numbers thats 10^3 so you have:

26^3 * 36 * 10^3 = 632,736,000 possibilities