Explanation The Counting Principle is a fundamental mathematical idea and an essential part of probability. Counting Principle/Rule states that, in a sequence of n events in which the first one has k 1 possibilities and the second event has k 2 and the third has k 3 , and so forth, the total number of possibilities of the sequence will be k 1 ⋅ k 2 ⋅ k 3 ⋅ k 4 ⋅ ⋅ ⋅ ⋅ k n So, we use the Counting Principle to determine the different unique ways we can do something, there are two cases explained below: Case 1: Events will affect each other (They are called dependent events, repetitions not allowed). Case 2: One event has no effect on the next event (They are called independent events, repetitions allowed). Here in our problem we have combination of case 1 and case 2 scenarios. If we consider the license plates with two letters followed by three digits where we have 26 ways of filling 1st letter, 26 ways of filling 2nd letter and 10 ways of filling 1st digit, 10 ways of filling 2nd digit, 10 ways of filling 3rd digit, we can set it up like when license plates with two letters followed by three digits, then L e t t e r s − A t o Z → ︸ L i c e n s e P l a t e ↗ 26 ︸ 1 s t × 26 ︸ 2 n d = 26 2 = 676 ways D i g i t − 0 t o 9 → ︸ L i c e n s e P l a t e ↗ 10 ︸ 3 r d × 10 ︸ 4 t h × 10 ︸ 5 t h = 10 3 = 1000 ways So total number of possible ways is 676 × 1000 , that is 676000 ways

College Algebra with Modeling and Visualization with Mymathlab Access Code

5th Edition

ISBN: 9780321869418

Author: Gary K. Rockswold

Publisher: PEARSON

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Chapter 8.3, Problem 8E

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The count of the number of possible license plates with two letters followed by three digits or four digits.

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Chapter 8.3, Problem 7E

Chapter 8.3, Problem 9E

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Chapter 8 Solutions

College Algebra with Modeling and Visualization with Mymathlab Access Code

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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