Question

The purpose of this discussion is to think about how the Counting Principle is used in creating license plates. STEP 1 A license plate is to consist of three digits, followed by two uppercase letters. Determine the number of license plates possible for each situation as well as give three examples of license plates which meet the criteria. • Repetition of numbers are letters is permitted. o Give three examples of license plates which meet the criteria. o Show your work for how many license plates are possible for that situation Repetition of numbers are letters is not permitted. Give three examples of license plates which meet the criteria. Show your work for how many license plates are possible for that situation. The first and second digits must be odd, and repetition of numbers and letters is not permitted. o Give three examples of license plates which meet the criteria. Show your work for how many license plates are possible for that situation. The first digit cannot be zero, and repetition of numbers and letters is not permitted Give three examples of icense plates which meet the criteria. Show your work for how many license plates are possible for that situation Create and post a similar questions regnes posted above for other hudents to try and answer. Try to answer other students cuestions

Answer 1

A license plate is to consist of three digits, followed by two uppercase letters. Repetition of numbers and letters is permitted. Each of the digits can be one of the {0, 1, 2, ...,8,9} and each of the letters can be from one of the 26 letters {A, B, C, ....YZ} Number of possible license plates = 10 x 10 x 10 x 26 x 26 = 676000 Three examples - (1) 011 AB, (2) 011XY, (3) 123MM

Repetition of numbers and letters is not permitted. First digit can be one of the {0, 1, 2, ...,8,9), second digit can be any of the remaining 9 numbers and lastly last digit can be any of the remaining 8 numbers. First letter can be from one of the 26 letters {A, B, C, ... ,Y,Z} and the second letter can be any of the remaining 25 letters. Number of possible license plates = 10 x 9 x 8 x 26 x 25 = 468000 Three examples - (1) 012AB, (2) 023XY, (3) 123MN

The first and second digits must be odd and repetition of numbers and letters is not permitted. First digit can be one of the {1,3,5,7,9), second digit can be any of the remaining 4 numbers and lastly last digit can be any of the remaining 8 numbers. First letter can be from one of the 26 letters {A, B, C, ...,Y,Z} and the second letter can be any of the remaining 25 letters. Number of possible license plates = 5 x 4 x 8 x 26 x 25 = 104000 Three examples - (1) 132AB, (2) 352XY, (3) 315MN

The first digit can not be zero and repetition of numbers and let- ters is not permitted. First digit can be one of the {1,2,3,...,8,9), second digit can be any of the remaining 9 numbers including 0) and lastly last digit can be any of the remaining 8 numbers. First letter can be from one of the 26 letters {A, B, C, ... ,Y,Z} and the second letter can be any of the remaining 25 letters. Number of possible license plates = 9 x 9 x 8 x 26 x 25 = 421200 Three examples - (1) 125AB, (2) 102XY (3) 415MN

Problem 1 : First digit is odd, second digit is 0 and last digit is even. Repetition of letters are allowed but repetition of numbers is not permitted. Solution : First digit can be one of the {1,3,5,7,9}, second digit is O and lastly last digit can be any of the 4 numbers 2,4,6,8} First and second letters can be from one of the 26 letters {A, B, C, ...,Y,Z}. Number of possible license plates = 5x1 x 4 x 26 x 26 = 13520 Three examples - (1) 102AA, (2) 102XY (3) 304PO