In a certain state, each automobile license plate number consists of two letters followed by a five-digit number.To avoid confusion between "O" and "zero" and "I" and "one", the letters "O" and "I" are not used.How many distinct license plate numbers can be formed?
A) 13,824,000
B) 57,600,000
C) 331,776,000
D) 5,760,000
E) 138,240,000

Question

Quizplus · Accepted Answer

There are 24 letters in the alphabet excluding I and O.
Thus, there are 24 choices for the first letter and 23 for the second letter.
So, there are $24*23=552$ ways to choose the two letters.
For each choice of letters, there are $10^5=100,000$ ways to choose a five-digit number.
Therefore, the total number of distinct license plate numbers is $552*100,000=55,200,000$.
So the answer is B.

In a Certain State, Each Automobile License Plate Number Consists