Answer the questions based on the following information. Hirawala is a uber rich guy who lives in a swanky place, called Hiranandini, in Mumbai. He has 15 diamond rings and 5 daughters.
If the rings are identical, find the number of ways of distributing these rings among his 5 daughters such that elder the daughter fewer the rings she gets. Thus the youngest daughter gets just 5 rings and the eldest daughter gets only 1 ring. No any two daughters are of the same age.

Options

A. 1
B. 5
C. 15
D. 3

Answer

To solve the problem of distributing 15 identical diamond rings among 5 daughters such that the youngest daughter gets 5 rings and the eldest daughter gets only 1 ring, we can follow these steps:

### Step-by-Step Solution

1. **Understanding the Distribution**:
- We have 5 daughters, and we need to distribute the rings in such a way that the youngest daughter (D5) gets the most rings (5 rings), and the eldest daughter (D1) gets the least (1 ring).
- The distribution of rings will be as follows:
- D5 (youngest) = 5 rings
- D4 = 4 rings
- D3 = 3 rings
- D2 = 2 rings
- D1 (eldest) = 1 ring

2. **Total Rings Calculation**:
- Let's calculate the total number of rings distributed:
- Total rings = 5 + 4 + 3 + 2 + 1 = 15 rings
- This matches the total number of rings Hirawala has, which is 15.

3. **Identical Rings**:
- Since all the rings are identical, the distribution is fixed. There are no variations in how the rings can be given to each daughter because the number of rings each daughter receives is predetermined.

4. **Counting the Ways**:
- Since the distribution is fixed (1 way to give 5 rings to D5, 4 rings to D4, 3 rings to D3, 2 rings to D2, and 1 ring to D1), there is only **1 way** to distribute the rings according to the given conditions.

5. **Conclusion**:
- Therefore, the total number of ways to distribute the rings among the daughters, given the constraints, is **1**.

### Final Answer:
The total number of ways to distribute the rings is **1**.

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