How Many 4-Digit Numbers Between 3000 and 5000 Can Be Formed Using Specific Digits Without Repetition?

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Introduction to the Problem

The task is to determine how many 4-digit numbers between 3000 and 5000 can be formed using the digits 0, 1, 2, 3, 4, 5, and 6 without repetition. This problem requires careful consideration of the constraints on the first digit and the digits that can follow.

Step-by-Step Breakdown

The first digit must be 3 or 4 to ensure the number falls within the range 3000-5000.

Case 1: First Digit is 3

When the first digit is 3:

Remaining digits available: 0, 1, 2, 4, 5, 6 (6 choices). Next, choose 3 more digits from these 6: Second digit can be any of the remaining 6 digits. Third digit can be chosen from the remaining 5 digits. Fourth digit can be chosen from the remaining 4 digits.

Calculating the number of combinations:

Total combinations: 6 × 5 × 4 120

Case 2: First Digit is 4

When the first digit is 4:

Remaining digits available: 0, 1, 2, 3, 5, 6 (6 choices). As in Case 1, the reasoning is the same: Second digit can be any of the remaining 6 digits. Third digit can be chosen from the remaining 5 digits. Fourth digit can be chosen from the remaining 4 digits.

Calculating the number of combinations:

Total combinations: 6 × 5 × 4 120

Total Combinations

Summing the valid combinations from both cases gives:

120 (for first digit 3) 120 (for first digit 4) 240

Thus, the total number of 4-digit numbers between 3000 and 5000 that can be formed using the digits 0, 1, 2, 3, 4, 5, and 6 without repetition is 240.

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By following these SEO practices, the article can attract more visitors who are searching for information on similar number formation problems and improve its visibility on search engines like Google.