10,108,800 assuming that leading 0s are not allowed in the 3-digit numbers; that the licence authorities do not block some letter combinations because they are rude, and letters that might be confused with numbers (O and 0, I and 1, Z and 2, S and 5, B and 8) are all permitted.
If repetitions are allowed, the number of possible ID cards can be calculated by taking the number of choices for each character. There are 26 letters and 10 digits, so the total combinations are (26^5 \times 10^2 = 11,881,376,000). If repetitions are not allowed, the calculation changes: for the letters, there are 26 options for the first letter, 25 for the second, and so on, resulting in (26 \times 25 \times 24 \times 23 \times 22). For the digits, there are 10 choices for the first digit and 9 for the second, leading to (10 \times 9). Thus, the total combinations without repetition are (26 \times 25 \times 24 \times 23 \times 22 \times 10 \times 9 = 3,263,200,000).
Allowing repetitions, there are 9 combinations. Without repeated digits, there is only one combination of 3 digits from 3.
If it alternates and you start with a letter, then there are 11,232,000 permutations. Then if you start with a number and alternate, there are another 11,232,000 permutations, for a total of 22,464,000 permutations. If you exclude the letters I, S, B, and O (because they look kind-of like 1, 5, 8, & 0 - kind-of important on license plates) then you are down to 6,652,800 & 13,305,600 respectively.
11,232,000
There are 26 possible letters and 10 possible numbers. The number of license plates possible is then 26*26*10*10*10*10 = 6760000.
12
How many license plates can be made using either two uppercase English letters followed by four digits or two digits followed by four uppercase English letters?
2600
Allowing repetitions, there are 9 combinations. Without repeated digits, there is only one combination of 3 digits from 3.
There are 676,000 ways to make the license plates.
3 decimal digits without repeats can form (10 x 9 x 8) = 720 distinct displays.For each of these . . .3 letters without repeats can form (26 x 25 x 24) = 15,600 distinct displays.Combine them on one plate, and there are (720) x (15,600) = 11,232,000 distinct displays available.
This depends on if you want repeats or not (or the state you are in) with repeats it is: 26x26x26x10x10= 1,757,600 without repeats it is: 26x25x24x10x9=1,560,000
If it alternates and you start with a letter, then there are 11,232,000 permutations. Then if you start with a number and alternate, there are another 11,232,000 permutations, for a total of 22,464,000 permutations. If you exclude the letters I, S, B, and O (because they look kind-of like 1, 5, 8, & 0 - kind-of important on license plates) then you are down to 6,652,800 & 13,305,600 respectively.
11,232,000
There are 26 possible letters and 10 possible numbers. The number of license plates possible is then 26*26*10*10*10*10 = 6760000.
There are 5*4*3 = 60 such numbers.
(26) x (26) x (10,000) = 6,760,000