How many distinct arrangements are possible for wearing five different rings in the five fingers of the right hand? (We can wear multiple rings in one finger)
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[*] $\frac{10!}{5!}$   


 [*] $5^5$

[*] $\frac{9!}{4!}$
[*] None of these

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To determine the number of distinct arrangements for wearing five different rings on the five fingers of the right hand, we need to consider the following:

1. **Understanding the problem**:
   - We have 5 different rings.
   - We have 5 fingers.
   - Each ring can be placed on any of the 5 fingers.
   - Multiple rings can be worn on the same finger.

2. **Applying the multiplication principle**:
   - For each ring, there are 5 choices (one for each finger).
   - Since the placement of each ring is independent of the others, we multiply the number of choices for each ring.

3. **Calculating the total number of arrangements**:
   - For the first ring, there are 5 choices.
   - For the second ring, there are 5 choices.
   - For the third ring, there are 5 choices.
   - For the fourth ring, there are 5 choices.
   - For the fifth ring, there are 5 choices.

   Therefore, the total number of distinct arrangements is:
   \[
   5 \times 5 \times 5 \times 5 \times 5 = 5^5
   \]

4. **Verification**:
   - The order in which the rings are placed on the fingers does not matter in this context because each ring is independently placed on any of the 5 fingers.
   - The formula \(\binom{5}{1} \cdot 5 \cdot \binom{4}{1} \cdot 4 \cdot \binom{3}{1} \cdot 3 \cdot \binom{2}{1} \cdot 2 \cdot \binom{1}{1} \cdot 1\) is not applicable here because it assumes a different context where the order of selection and placement is considered differently.

The final answer is \(\boxed{5^5}\).