The state of Illinois is redesigning their standardized license plates to also i

Question

The state of Illinois is redesigning their standardized license plates to also

include an asterisk (*) in-addition to the original 7 alphanumeric characters (both

letters and numbers). How many unique license plates can be generated using this

new rule? Use Combinatorics to solve this problem.

- Repetition is allowed. Meaning, that if the letter 'A' is used in the a license plate, it can be used again in any of the other available slots. (Think back to the tree structure we worked out in class with listing possible combinations)

- You do not need to account upper and lower case letters for this problem, Meaning, that the letters 'A' and 'a' are not considered different characters. For this problem, assume that all letters are uppercase.

- the additional asterisk character that has been added to the problem does not mean that we now have 8 slots to fill, but rather 7 slots, as the problem states, which each slot now has the potential to either be a letter, a number, or the asterisk.

Please take dash notes into consideration.

Explanation / Answer

Since we have 7 slots only and to fill the 7 slots initialy we had the choice of alpha numerics only but now we have ana additional choice of * also

So we have total choice available for each slot is

Alphabets = 26(Since we have to use capital letters only)

numerics = 10 ( from 0 to 9)

Special character "*" =1

So total choices available = 26+10 +1

As given we can repeat any alphanumeric or * any times so ultimately we have total 37 choices for each slot which makes total choices = 37 * 37 *37 * 37 *37 * 37 *37 = 37^7 total choices available

So., 37^7unique license plates can be generated using this new rule

Hope the above ans has helped you in understanding the problem pls upvote if it has really helped you. Good Luck!!

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