To solve this question, let’s break it into steps based on the given problem and solution:

Question Recap:

We are tasked to find how many five-digit numbers are possible if the number is greater than 40,000 and digits cannot be repeated.

Step-by-Step Solution:

1. Analyze the first digit:

   • To ensure the number is greater than 40,000, the first digit (most significant) must be 4, 5, 6, 7, 8, or 9. That gives 6 options.

2. Second digit selection:

   • Once the first digit is chosen, we have 9 remaining digits to pick from (since repetition is not allowed). This gives 9 options for the second digit.

3. Third digit selection:

   • After selecting the first and second digits, 8 digits remain to choose from, so there are 8 options for the third digit.

4. Fourth digit selection:

   • Now, 7 digits remain, providing 7 options for the fourth digit.

5. Fifth digit selection:

   • Finally, 6 digits remain, so there are 6 options for the fifth digit.

Total Calculation:

The total number of five-digit numbers is:

$6 \times 9 \times 8 \times 7 \times 6 = 2,160$

This matches the solution provided in the image.

Final Answer:

There are 2,160 five-digit numbers greater than 40,000 where digits cannot be repeated.

Let me know if you'd like further clarification or additional examples.
Here are 5 related questions for practice:

1. How many five-digit numbers less than 50,000 can be formed without repeating digits?
2. What is the total number of five-digit numbers possible without repeating digits?
3. How many six-digit numbers greater than 100,000 can be formed without repeating digits?
4. What happens to the count if the restriction of non-repeating digits is removed?
5. How many numbers greater than 40,000 can be formed if only odd digits are allowed?

Tip: Always identify and limit the options for the most restrictive digit(s) first when solving digit-based problems.