A person X has four notes of rupee 1, 2, 5 and 10 denomination. The number of different sums of money she can form from them is

Options

A. 16
B. 15
C. 12
D. 8

Answer

To find the number of different sums of money that person X can form using the notes of denominations 1, 2, 5, and 10, we can follow these steps:

### Step 1: Identify the denominations
The denominations of the notes are:
- 1 rupee
- 2 rupees
- 5 rupees
- 10 rupees

### Step 2: Determine the possible combinations
Each note can either be included in a sum or not included. This means for each note, there are 2 choices: to take it or to leave it. Since there are 4 notes, the total number of combinations can be calculated as:
\[ 2^n \]
where \( n \) is the number of notes.

### Step 3: Calculate the total combinations
In this case, \( n = 4 \):
\[ 2^4 = 16 \]
This means there are 16 combinations of notes, including the case where no notes are selected.

### Step 4: Exclude the empty combination
Since we are interested in different sums of money, we need to exclude the combination where no notes are selected (which gives a sum of 0). Therefore, we subtract 1 from the total combinations:
\[ 16 - 1 = 15 \]

### Step 5: List the possible sums
To ensure that we have counted all possible sums correctly, we can list the sums formed by different combinations of the notes:
1. Using no notes: 0 (excluded)
2. Using only 1 rupee: 1
3. Using only 2 rupees: 2
4. Using only 5 rupees: 5
5. Using only 10 rupees: 10
6. Using 1 and 2 rupees: 3
7. Using 1 and 5 rupees: 6
8. Using 1 and 10 rupees: 11
9. Using 2 and 5 rupees: 7
10. Using 2 and 10 rupees: 12
11. Using 5 and 10 rupees: 15
12. Using 1, 2, and 5 rupees: 8
13. Using 1, 2, and 10 rupees: 13
14. Using 1, 5, and 10 rupees: 16
15. Using 2, 5, and 10 rupees: 17
16. Using all notes: 18

### Conclusion
After listing all possible sums, we confirm that the total number of different sums that can be formed is indeed 15.

### Final Answer
The number of different sums of money she can form is **15**.

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