Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
**License Plate Arrangement Problem** **Problem Statement:** Suppose you want to get a license plate. The license plate has to have 3 letters without repetition, followed by 5 numbers without repetition. How many arrangements are possible? **Options:** - a) 78,624,000 - b) 15,600 - c) 471,744,000 - d) 30,240 **Explanation:** To solve this problem, consider the following: 1. **Letters:** Since the plate requires 3 letters without repetition from the English alphabet (26 letters), the number of possible arrangements for the letters is calculated as: - First letter: 26 choices - Second letter: 25 choices (since one letter is already used) - Third letter: 24 choices (since two letters are already used) Total arrangements for letters = 26 × 25 × 24 2. **Numbers:** The plate requires 5 numbers without repetition (from the digits 0-9), so the number of possible arrangements for the numbers is calculated as: - First number: 10 choices - Second number: 9 choices (since one number is already used) - Third number: 8 choices (since two numbers are already used) - Fourth number: 7 choices (since three numbers are already used) - Fifth number: 6 choices (since four numbers are already used) Total arrangements for numbers = 10 × 9 × 8 × 7 × 6 **Total Arrangements:** Multiply the arrangements for letters by the arrangements for numbers to find the total possible license plate configurations.
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Transcribed Image Text:**License Plate Arrangement Problem** **Problem Statement:** Suppose you want to get a license plate. The license plate has to have 3 letters without repetition, followed by 5 numbers without repetition. How many arrangements are possible? **Options:** - a) 78,624,000 - b) 15,600 - c) 471,744,000 - d) 30,240 **Explanation:** To solve this problem, consider the following: 1. **Letters:** Since the plate requires 3 letters without repetition from the English alphabet (26 letters), the number of possible arrangements for the letters is calculated as: - First letter: 26 choices - Second letter: 25 choices (since one letter is already used) - Third letter: 24 choices (since two letters are already used) Total arrangements for letters = 26 × 25 × 24 2. **Numbers:** The plate requires 5 numbers without repetition (from the digits 0-9), so the number of possible arrangements for the numbers is calculated as: - First number: 10 choices - Second number: 9 choices (since one number is already used) - Third number: 8 choices (since two numbers are already used) - Fourth number: 7 choices (since three numbers are already used) - Fifth number: 6 choices (since four numbers are already used) Total arrangements for numbers = 10 × 9 × 8 × 7 × 6 **Total Arrangements:** Multiply the arrangements for letters by the arrangements for numbers to find the total possible license plate configurations.
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