Amanda W. asked • 09/13/15
How many license plates can be produced using five symbols on each plate where the first two symbols are letters of the alphabet and the following three symbols are numbers selected from the set ?{0,1,2,3,4,5,6,7,8,9}? No number or letter can be repeated on the same license plate.
If letters and numerals can be repeated, it will in fact be $36^6$. For each of the six slots, we have 36 choices for what can go there. By the rule of product, there are then $36\cdot 36\cdot 36\cdot 36\cdot 36\cdot 36=36^6$ different such license plates. If letters and numerals cannot be repeated, you will have 36 choices for the first slot, 35 choices for the second, 34 for the third,... for a total of $36\cdot 35\cdot 34\cdot 33\cdot 32\cdot 31 = \frac{36!}{30!}$ I'll leave the final one to you to think about, but again, try to break it up via rule of product by figuring out how many choices there are for the first spot, how many choices for the second, how many choices for the third, etc... and multiply those numbers together. Recommended textbooks for you  Algebra & Trigonometry with Analytic Geometry College Algebra (MindTap Course List) Author:R. David Gustafson, Jeff Hughes Publisher:Cengage Learning College Algebra Publisher:Cengage Learning College Algebra Algebra: Structure And Method, Book 1 Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole Publisher:McDougal Littell Algebra & Trigonometry with Analytic Geometry ISBN:9781133382119 Author:Swokowski Publisher:Cengage College Algebra (MindTap Course List) ISBN:9781305652231 Author:R. David Gustafson, Jeff Hughes Publisher:Cengage Learning College Algebra ISBN:9781337282291 Author:Ron Larson Publisher:Cengage Learning College Algebra ISBN:9781938168383 Author:Jay Abramson Publisher:OpenStax Algebra: Structure And Method, Book 1 ISBN:9780395977224 Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole Publisher:McDougal Littell |
How many 5 character license plates are possible if the first three characters must be letters the last two must be digits 0 9 and repeated characters are allowed?
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