In a certain state, each automobile license plate number consists of two letters followed by a four-digit number. To avoid confusion between "O" and zero and between "I" and one, the letters "O" and "I" are not used. How many distinct license plates can be formed in this state?

Question

In a certain state, each automobile license plate number consists of two letters followed by a four-digit number.  To avoid confusion between "O" and zero and between "I" and one, the letters "O" and "I" are not used.  How many distinct license plates can be formed in this state?

Damon · Answer

26 letters - 2 = 24 letters

choice of 24 letters for first letter
since letters can be repeated we have 24*24 = 576 letter combinations

now we have ten numbers, 0 through 9
again they can be repeated
(AA0000 is allowed)
10^4 = 10,000
so
576 * 10,000 = 5.76 * 1,000,000
= 5,760,000

Anonymous · Answer

If aplate