The number of possible plates that can be made is 14,601,600
We shall consider every of the possible choices one after the other.
For the numerals, we are selecting from the digits 0-9 ( total 10 choices)
For the letters, we are selecting from A-Z (total 26 choices)
For the first X, we are to select 1 number from 0-9
This means we are having a selection equal to 10 C 1 ( read as 10 combination 1)
For the first L , we have no restrictions
We are to select an alphabet from among A-Z.
The number of possible choices here will be 26 C 1
For the second L, we have no restriction
The number of possible choices here will be 26 C 1
For the third L, we have a restriction
The restriction is that the letter selected cannot be S or O
What this means is that out of our 26, we do not have any business with 2 letters. So we are left with 24 alphabets to select from
The number of possible choices here will be 24 C 1
For the second X, we have a restriction
The second numeral cannot be 0
So we are to select a digit from 9 digits
The number of possible choices here will be 9 C 1
For the last X , we have no restrictions
The number of possible ways here will be;
10 C 1
To get the overall number of possible plates, we have to multiply all the choices here together
Mathematically, for a range of numbers totaling n from which we want to select a single value, the number of ways this can be done is n C 1 ways and it is equal to n
Thus, for each of our choices above, we simply will have the preceeding number as the number of ways
Hence, the total number of possible plate numbers will be;
10 * 26 * 26 * 24 * 9 * 10 = 14,601,600