Problem:
A license plate in a certain state consists of digits, not necessarily distinct, and letters, also not necessarily distinct. These six characters may appear in any order, except that the two letters must appear next to each other. How many distinct license plates are possible?
Answer Choices:
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Solution:
Since the two letters have to be next to each other, think of them as forming a two-letter word . So each license plate consists of digits and . For each digit there are choices. There are choices for the letters of , and there are choices for the position of . So the total number of distinct license plates is .
The problems on this page are the property of the MAA's American Mathematics Competitions