If a secretary and a joint secretary are to be selected from a committee of 11 members, then in how many ways can they be selected

Options

A. 110
B. 55
C. 22
D. 11

Answer

To solve the problem of selecting a secretary and a joint secretary from a committee of 11 members, we will follow these steps:

### Step 1: Understand the roles
We need to select two different positions: a secretary and a joint secretary. Since these positions are distinct, the order in which we select the members matters.

### Step 2: Select the secretary
We can choose any one of the 11 members to be the secretary. Therefore, there are 11 possible choices for the secretary.

### Step 3: Select the joint secretary
Once the secretary has been chosen, we cannot select the same person for the joint secretary position. This leaves us with 10 remaining members to choose from for the joint secretary position.

### Step 4: Calculate the total number of ways
To find the total number of ways to select both the secretary and the joint secretary, we multiply the number of choices for each position:

\[ \text{Total ways} = (\text{Choices for Secretary}) \times (\text{Choices for Joint Secretary}) = 11 \times 10 \]

### Step 5: Perform the multiplication
Now, we perform the multiplication:

\[ 11 \times 10 = 110 \]

### Conclusion
Thus, the total number of ways to select a secretary and a joint secretary from a committee of 11 members is **110**.

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