Five persons including one lady are to deliver lectures to an audience. The organiser can arrange the lecture so that the lady is always in the middle in

Options

A. 120 ways
B. 96 ways
C. 24 ways
D. 5 ways

Answer

To solve the problem, we need to determine the number of ways to arrange five persons (including one lady) such that the lady is always in the middle position.

### Step-by-Step Solution:

1. **Identify the Positions**:
Since there are five persons, we can denote their positions as 1, 2, 3, 4, and 5. The middle position is position 3.

2. **Fix the Lady's Position**:
We will place the lady in the middle position (position 3). This is a fixed position, so we do not need to consider arrangements for her.

3. **Arrange the Remaining Persons**:
After placing the lady in the middle, we have four remaining persons to arrange in the remaining positions (1, 2, 4, and 5).

4. **Calculate the Arrangements**:
The number of ways to arrange 4 persons in 4 positions is given by the factorial of the number of persons. Therefore, we calculate:
\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]

5. **Final Answer**:
Thus, the total number of arrangements of the five persons with the lady in the middle is 24.

### Summary:
The total number of ways to arrange the five persons such that the lady is always in the middle is **24**.