Using the integers 4,7,9,8 and 5, how many two digit numbers can be formed if repletion is NOT allowed

To solve this problem, we need to find how many two-digit numbers can be formed using the integers 4, 7, 9, 8, and 5 without repetition.

### Step-by-step breakdown:
1. A two-digit number consists of two places: the tens place and the units place.
2. For the tens place, we have 5 available digits (4, 7, 9, 8, 5) to choose from.
3. After choosing a digit for the tens place, we cannot repeat it in the units place. This means we have 4 remaining digits to choose from for the units place.

### Calculation:
- For the tens place, we have 5 choices.
- For the units place, we have 4 choices (since repetition is not allowed).

Thus, the total number of two-digit numbers is:
\[
5 \times 4 = 20
\]

### Conclusion:
The total number of two-digit numbers that can be formed using the digits 4, 7, 9, 8, and 5 without repetition is **20**.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How many three-digit numbers can be formed using the same digits without repetition?
2. What if repetition is allowed? How many two-digit numbers can be formed then?
3. How many odd two-digit numbers can be formed without repetition using these digits?
4. What is the largest two-digit number that can be formed using these digits without repetition?
5. How many two-digit numbers can be formed if the first digit cannot be 4?

**Tip:** For combinatorics problems, think about the number of choices available at each step and whether repetition is allowed or not!

Find out how many two-digit numbers can be formed using the digits 4, 7, 9, 8, and 5 without repetition. This combinatorics problem demonstrates the principles of permutations, offering a step-by-step solution suitable for Grades 6-8.

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