Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 10 Counting Methods and Probability - 10.1 Apply the counting Principles and Permutations - 10.1 Exercises - Skill Practice - Page 687: 17

Answer

Option A

Work Step by Step

Because the English alphabet has 26 letters, there are 26 alternatives for the first letter. Because the letters cannot be repeated, the second letter can be picked in one of 25 possible ways. There are a total of ten different digits. For the first one, there are ten possible alternatives. Because they can't be repeated, the second one can be picked in nine different ways; the third in eight; and the fourth in seven. Hence, the number of license plates is: $26\times25\times10\times9\times8\times7=3.276.000$ Thus, the correct answer is A.
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