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? a 78,624,000 15,600 471,744,000 d. 30,240
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? a 78,624,000 15,600 471,744,000 d. 30,240
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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