In how many ways a garland can be made by using 15 different flowers.

Options

A. `lfloor(10)`
B. `lfloor(9)`
C. `2lfloor(9)`
D. `lfloor(14)//2`

Answer

To determine the number of ways to make a garland using 15 different flowers, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Circular Permutation**:
- When arranging items in a circle, one item can be fixed to eliminate the effect of rotations. This is because rotating the entire arrangement does not create a new arrangement.

2. **Fixing One Flower**:
- We can fix one flower in place. This leaves us with 14 flowers to arrange around the fixed flower.

3. **Arranging the Remaining Flowers**:
- The number of ways to arrange the remaining 14 flowers is given by the factorial of the number of flowers, which is \(14!\).

4. **Accounting for Direction**:
- Since a garland can be viewed from both clockwise and anti-clockwise directions, arrangements that are mirror images of each other should not be counted twice. Therefore, we need to divide the total arrangements by 2.

5. **Final Calculation**:
- The total number of ways to arrange the garland is given by:
\[ \text{Total arrangements} = \frac{14!}{2} \]

### Final Answer:
Thus, the number of ways to make a garland using 15 different flowers is \(\frac{14!}{2}\).