Aseries of specialty license plates consists of three digits followed by two letters. how many unique license plates are possible? a. 234,000 b. 468,000 c. 676,000 d. 1,757,600

The Answer is c: 676,000

There are 26 choices for the first letter. For each of these letters, there are 26 choices for the second letter. There are therefore 26X26 = 676 possible pairs of letters. (Note that a repeat letter, such as DO, is allowed aid so we do not use₂₆P₂.) You must now consider the three numbers. There are 10.possibilities for the first digit, 10 possibilities for the second, and 10 possibilities for the third. This means that there are 10 x 10 x10 = 1000 different numbers. (Note that this is simply saying that there are 1000 numbers between and including 000 and 999.)
Combining these results, it follows that there are 676 x 1000 = 676,000 different license plates possible.