Counting 2. In Ontario, commercial vehicle license plates currently have the format XX NNNNN, where XX are letters and NNNNN are numbers. A sample image is shown on the right. We are interested in how many license plates remain in this series. We assume that all license plate combinations in this format are eligible to be issued a license (i.e., no plates are skipped or left out for any reason). ONTARIO SEP AJ-42864 YOURS TO DISCOVER A sample Ontario Commercial License Plate (by Dvermeirre - CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curi d=42644451) a. How many total commercial license plate combinations are available in the format above? That is, how many total license plates can be formed for the above format, starting at AA 00000 and going to ZZ 99999? Give a short explanation for how you arrived at this quantity. b. Assume that all plates are released in order, so that AA 00000 is the first plate to be issued, then all plates of the form AA NNNNN (in numerical order) then AB 00000, then all plates of the form AB NNNNN, etc. For this part of the question, you are asked to use your initials to calculate how many license plates combinations remain after the plate XY N1337, where XY are your initials and N is the last digit in the date of your birthday. So, if you were born on the 13th of the month, the number N should be 3. If you were born on the 5th of the month, the number N should be 5. - For this question, choose a pair of initials that represents your name in some way. (So if you have three initials, pick two letters; if you have a name that you use that is different from your birth name, feel free to use that, etc.) - By "after" in this question, we mean that you should assume that the plate XY 01337 has been issued already, and the next plate to be issued is XY 01338. This is the first plate after XY 01337. For your initials and birth date digit, give the number of license plate combinations that come after XY N1337. Give the final number, plus an explanation of how it works, including breaking the quantity down into sections that illustrate how you arrived at your answer. Make sure to clearly indicate in your response your "personal" plate number that serves at the starting point - failure to do so will result in lost marks. If it is helpful, here's a table that shows the number of letters in the alphabet that are after a given letter. A B с D E F G H J 25 24 23 22 21 20 19 18 17 16 K L M N P Q R S T 15 14 13 12 11 10 9 8 7 6 U V W X Y Z 5 4 3 2 1 0