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

Answer

To solve the problem of how many ways a garland can be made using 15 different flowers, we can follow these steps:

### Step 1: Understand the Problem
We need to arrange 15 different flowers in a circular manner to form a garland.

### Step 2: Use the Formula for Circular Permutations
When arranging \( n \) different objects in a circle, the number of arrangements is given by the formula:
\[ (n - 1)! \]
This is because one object can be fixed to break the circular symmetry, allowing us to arrange the remaining \( n - 1 \) objects linearly.

### Step 3: Apply the Formula
In our case, we have \( n = 15 \) different flowers. Therefore, the number of ways to arrange these flowers in a circular manner is:
\[ (15 - 1)! = 14! \]

### Step 4: Conclusion
Thus, the total number of ways to make a garland using 15 different flowers is:
\[ 14! \]

### Final Answer
The answer is \( 14! \).

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