The total number of ways in which a beggar can be given at least one rupee from four 25-paisa coins, three 50-paisa coins and 2 one-rupee coins, is:

Options

A. 54
B. 51
C. 53
D. 52

Answer

To solve the problem of how many ways a beggar can be given at least one rupee from four 25-paisa coins, three 50-paisa coins, and two one-rupee coins, we can follow these steps:

### Step 1: Identify the coins and their values
- We have:
- 4 coins of 25 paisa (0.25 rupees)
- 3 coins of 50 paisa (0.50 rupees)
- 2 coins of 1 rupee (1.00 rupee)

### Step 2: Calculate the total combinations without restrictions
For each type of coin, we can choose from 0 to the maximum number available:
- For 25-paisa coins: We can choose 0, 1, 2, 3, or 4 coins. This gives us 5 options (0 to 4).
- For 50-paisa coins: We can choose 0, 1, 2, or 3 coins. This gives us 4 options (0 to 3).
- For 1-rupee coins: We can choose 0, 1, or 2 coins. This gives us 3 options (0 to 2).

Thus, the total number of combinations is:
\[ 5 \text{ (for 25-paisa)} \times 4 \text{ (for 50-paisa)} \times 3 \text{ (for 1-rupee)} = 60 \]

### Step 3: Subtract the cases where the beggar receives less than 1 rupee
The beggar can receive:
- 0 rupees (no coins)
- 25 paisa (1 coin of 25 paisa)
- 50 paisa (1 coin of 50 paisa)
- 75 paisa (3 coins of 25 paisa or 1 coin of 50 paisa and 1 coin of 25 paisa)

Now, let's calculate the combinations for each of these cases:
1. **0 rupees**: 1 way (no coins).
2. **25 paisa**: 4 ways (choosing any one of the four 25-paisa coins).
3. **50 paisa**: 3 ways (choosing any one of the three 50-paisa coins).
4. **75 paisa**:
- Choosing 3 coins of 25 paisa: 1 way.
- Choosing 1 coin of 50 paisa and 1 coin of 25 paisa: 3 ways (choose any one of the three 50-paisa coins and any one of the four 25-paisa coins).

Thus, the total combinations for less than 1 rupee:
\[ 1 \text{ (0 rupees)} + 4 \text{ (25 paisa)} + 3 \text{ (50 paisa)} + (1 + 12) \text{ (75 paisa)} = 1 + 4 + 3 + 13 = 21 \]

### Step 4: Calculate the total combinations for at least 1 rupee
To find the number of ways to give at least 1 rupee, we subtract the cases where the beggar receives less than 1 rupee from the total combinations:
\[ 60 - 21 = 39 \]

### Final Answer
The total number of ways in which a beggar can be given at least one rupee is **39**.