If `1!9 = 20, 9!5 = 28 and 5!5 = 20`, then find the value of `7!3` = ?

Options

A. 20
B. 15
C. 22
D. 24

Answer

To solve the problem, we need to identify the pattern in the given equations and apply it to find the value of \( 7!3 \).

### Step-by-Step Solution:

1. **Identify the Pattern:**
We have three equations:
- \( 1!9 = 20 \)
- \( 9!5 = 28 \)
- \( 5!5 = 20 \)

Let's analyze each equation to find a consistent pattern.

2. **Examine the First Equation:**
- For \( 1!9 = 20 \):
- Calculate \( 1 + 9 = 10 \)
- Then, multiply by 2: \( 10 \times 2 = 20 \)

3. **Examine the Second Equation:**
- For \( 9!5 = 28 \):
- Calculate \( 9 + 5 = 14 \)
- Then, multiply by 2: \( 14 \times 2 = 28 \)

4. **Examine the Third Equation:**
- For \( 5!5 = 20 \):
- Calculate \( 5 + 5 = 10 \)
- Then, multiply by 2: \( 10 \times 2 = 20 \)

5. **Apply the Pattern to \( 7!3 \):**
- Now, we need to find \( 7!3 \):
- Calculate \( 7 + 3 = 10 \)
- Then, multiply by 2: \( 10 \times 2 = 20 \)

6. **Final Result:**
- Therefore, \( 7!3 = 20 \).

### Conclusion:
The value of \( 7!3 \) is \( 20 \).