In how many ways can a chairman and vice - chairman be elected from a committee of 8 members who are equally eligible for the post ?

Answer

To solve the problem of how many ways a chairman and vice-chairman can be elected from a committee of 8 members, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Members**: We have a committee of 8 members.

2. **Choose the Chairman**: The first step is to select a chairman. Since there are 8 members, there are 8 possible choices for the chairman.

\[ \text{Ways to choose Chairman} = 8 \]

3. **Choose the Vice-Chairman**: After selecting the chairman, we need to choose a vice-chairman. Since the chairman cannot also be the vice-chairman, we have 7 remaining members to choose from.

\[ \text{Ways to choose Vice-Chairman} = 7 \]

4. **Calculate the Total Combinations**: The total number of ways to choose both a chairman and a vice-chairman is the product of the number of ways to choose each position.

\[ \text{Total Ways} = \text{Ways to choose Chairman} \times \text{Ways to choose Vice-Chairman} = 8 \times 7 = 56 \]

5. **Final Answer**: Therefore, the total number of ways to elect a chairman and a vice-chairman from the committee of 8 members is 56.

### Summary:
The total number of ways to elect a chairman and a vice-chairman from a committee of 8 members is **56**.

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