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You have a driver's license that has to have 3 digits followed by 4 letters. Find the total number of outcomes available with the repetition of digits and letters. Use the Fundamental Counting Principle to calculate this. a 258,336,000 b 175,760,000 456,976,000 78,624,000

You have a driver's license that has to have 3 digits followed by 4 letters. Find the total number of outcomes available with the repetition of digits and letters. Use the Fundamental Counting Principle to calculate this. a 258,336,000 b 175,760,000 456,976,000 78,624,000

Advanced Engineering Mathematics
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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**Problem Statement:** You have a driver's license that must have 3 digits followed by 4 letters. Find the total number of outcomes available with the repetition of digits and letters. Use the Fundamental Counting Principle to calculate this. **Options:** - a) 258,336,000 - b) 175,760,000 - c) 456,976,000 - d) 78,624,000 **Explanation:** To find the total number of outcomes: 1. **Digits**: There are 10 possibilities for each digit (0-9). - Total outcomes for 3 digits = 10 × 10 × 10 = 1,000 2. **Letters**: There are 26 possibilities for each letter (A-Z). - Total outcomes for 4 letters = 26 × 26 × 26 × 26 = 456,976 3. **Combined Outcome**: Multiply the outcomes for digits and letters. - Total = 1,000 × 456,976 = 456,976,000 Therefore, the correct answer is option **c) 456,976,000**.
Transcribed Image Text:**Problem Statement:** You have a driver's license that must have 3 digits followed by 4 letters. Find the total number of outcomes available with the repetition of digits and letters. Use the Fundamental Counting Principle to calculate this. **Options:** - a) 258,336,000 - b) 175,760,000 - c) 456,976,000 - d) 78,624,000 **Explanation:** To find the total number of outcomes: 1. **Digits**: There are 10 possibilities for each digit (0-9). - Total outcomes for 3 digits = 10 × 10 × 10 = 1,000 2. **Letters**: There are 26 possibilities for each letter (A-Z). - Total outcomes for 4 letters = 26 × 26 × 26 × 26 = 456,976 3. **Combined Outcome**: Multiply the outcomes for digits and letters. - Total = 1,000 × 456,976 = 456,976,000 Therefore, the correct answer is option **c) 456,976,000**.
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