Introduction:

In this problem, we are given 10 examination papers arranged in such a way that we need to find the number of 4 digit numbers greater than 5000 that can be formed using the digits 3, 4, 5, 6, and 7 without any repetition.

Solution:

To solve this problem, we can use the following steps:

1. Determine the total number of digits available: There are 5 digits available (3, 4, 5, 6, and 7) to form the 4-digit numbers.

2. Determine the number of ways to choose the first digit: Since the number has to be greater than 5000, the first digit can only be 5, 6, or 7. Therefore, there are 3 ways to choose the first digit.

3. Determine the number of ways to choose the second digit: Since we cannot repeat any digits, there are only 4 digits left to choose from. Therefore, there are 4 ways to choose the second digit.

4. Determine the number of ways to choose the third digit: Since we cannot repeat any digits, there are only 3 digits left to choose from. Therefore, there are 3 ways to choose the third digit.

5. Determine the number of ways to choose the fourth digit: Since we cannot repeat any digits, there are only 2 digits left to choose from. Therefore, there are 2 ways to choose the fourth digit.

6. Use the multiplication principle: The total number of 4-digit numbers greater than 5000 that can be formed using the digits 3, 4, 5, 6, and 7 without any repetition is given by:

3 x 4 x 3 x 2 = 72

Therefore, there are 72 such numbers.

Conclusion:

In conclusion, we have determined that the number of 4-digit numbers greater than 5000 that can be formed using the digits 3, 4, 5, 6, and 7 without any repetition is 72. This problem can be solved using the multiplication principle and the fact that we cannot repeat any digits.