Explanation
Step 1: Analyze the Letters
There are 26 English letters available. The license plate requires 3 letters, and repetitions are allowed.
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Number of ways to fill the 1st letter position = 26
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Number of ways to fill the 2nd letter position = 26
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Number of ways to fill the 3rd letter position = 26
Total ways for letters = 26×26×26=263
Step 2: Analyze the Digits
There are 10 digits available (0 through 9). The license plate requires 4 digits, and repetitions are allowed.
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Number of ways to fill the 1st digit position = 10
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Number of ways to fill the 2nd digit position = 10
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Number of ways to fill the 3rd digit position = 10
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Number of ways to fill the 4th digit position = 10
Total ways for digits = 10×10×10×10=104
Step 3: Apply the Fundamental Principle of Multiplication
Since the letters and the digits must both be chosen to complete the license plate, we multiply the possibilities:
Total License Plates=(Ways for Letters)×(Ways for Digits)
Total License Plates=263×104
Conclusion:
The total number of different license plates is 263×104.
Correct Option: (a)
