Sure, let's solve this step-by-step. We need to form five different 4-digit numbers using the digits 2, 3, 5, and 7. Importantly, each digit must be used exactly once in each of the numbers.
### Step 1: List all possible 4-digit numbers
By using the digits 2, 3, 5, and 7 exactly once, we can form various permutations. Some of the 4-digit numbers formed would be:
- 7532
- 7523
- 7352
- 7325
- 7253
- 7235
- 5732
- 5723
- 5372
- 5327
- 5273
- 5237
- 3752
- 3725
- 3572
- 3527
- 3275
- 3257
- 2753
- 2735
- 2573
- 2537
- 2375
- 2357
### Step 2: Select five different 4-digit numbers
From this pool of permutations, we can select any five. Let's choose the five largest numbers for this purpose.
### Step 3: Arrange the numbers in descending order
The five different 4-digit numbers using the digits 2, 3, 5, and 7, starting with the largest, are:
1. 7532
2. 7523
3. 7352
4. 7325
5. 7253
So, the final list of five different 4-digit numbers, sorted in descending order, is:
- 7532
- 7523
- 7352
- 7325
- 7253
