How many different amounts can be formed with one-one coin of Rs 1, Rs 2, Rs 5 and Rs 10?

Answer

To solve the problem of how many different amounts can be formed with one coin each of Rs 1, Rs 2, Rs 5, and Rs 10, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Coins**: We have the following coins:
- Rs 1
- Rs 2
- Rs 5
- Rs 10

2. **Count the Number of Coins**: There are a total of 4 coins.

3. **Understanding the Combinations**: Each coin can either be included in a sum or not. This gives us two choices (include or exclude) for each coin.

4. **Calculate Total Combinations**: The total number of combinations of these coins can be calculated using the formula:
\[ \text{Total combinations} = 2^n \]
where \( n \) is the number of coins. Here, \( n = 4 \).

5. **Apply the Formula**:
\[ \text{Total combinations} = 2^4 = 16 \]

6. **Exclude the Empty Set**: One of these combinations is the empty set (not choosing any coins), which does not contribute to a sum. Therefore, we subtract 1 from the total combinations:
\[ \text{Different amounts} = 16 - 1 = 15 \]

7. **Final Result**: Thus, the total number of different amounts that can be formed is 15.

### Summary of the Calculation:
- Total combinations of coins = \( 2^4 = 16 \)
- Subtract the empty set = \( 16 - 1 = 15 \)