From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?

Options

A. 1360
B. 1260
C. 1060
D. 1160

Answer

To solve the problem of appointing one principal and one vice-principal from among 36 teachers, we can follow these steps:

### Step 1: Choose the Principal
First, we need to select one principal from the 36 teachers. The number of ways to choose the principal is simply the total number of teachers available, which is 36.

**Hint:** Think about how many options you have for the first position (principal).

### Step 2: Choose the Vice-Principal
Once the principal has been chosen, we cannot select the same person for the vice-principal position. Therefore, we have 35 teachers left to choose from for the vice-principal.

**Hint:** After selecting the principal, consider how many teachers are left for the second position (vice-principal).

### Step 3: Calculate the Total Number of Ways
To find the total number of ways to appoint both the principal and the vice-principal, we multiply the number of choices for each position together:
\[ \text{Total ways} = (\text{Ways to choose Principal}) \times (\text{Ways to choose Vice-Principal}) = 36 \times 35 \]

### Step 4: Perform the Calculation
Now, we calculate:
\[ 36 \times 35 = 1260 \]

### Final Answer
Thus, the total number of ways to appoint one principal and one vice-principal from among the 36 teachers is **1260**.

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