A Five-Digit Number Formed Using 1 3 5 7 9
This is a classic permutation problem! We need to figure out how many different five-digit numbers we can form using the digits 1, 3, 5, 7, and 9.
Here's how we approach the problem:
Understanding Permutations
A permutation is an arrangement of objects in a specific order. In this case, we have 5 distinct digits and we want to arrange them into a five-digit number.
The Calculation
- For the first digit: We have 5 choices (1, 3, 5, 7, or 9).
- For the second digit: We've used one digit, so we have 4 choices left.
- For the third digit: We have 3 choices left.
- For the fourth digit: We have 2 choices left.
- For the fifth digit: We have only 1 choice left.
Therefore, the total number of permutations (five-digit numbers) is:
5 * 4 * 3 * 2 * 1 = 120
The Answer
There are 120 different five-digit numbers that can be formed using the digits 1, 3, 5, 7, and 9.
