Question

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

Answer 1

Hint: For solving this question, first we will see the concept of the fundamental principle of multiplication. After that, we will find the number of choices available for the post of principal and vice-principal, when we assign the post from 36 teachers in succession. Then, we will multiply the number of choices to get the final answer.

Complete step-by-step answer:
Given:
We have to find the number of ways we can appoint one principal and one vice-principal from 36 teachers in a school.
Now, before we proceed we should know the following important concept and formulas:
Fundamental Principle of Multiplication:
If there are two jobs such that one of them can be completed in $m$ ways, and when it has been completed in any of these $m$ ways, the second job can be completed in $n$ ways. Then, two jobs in succession can be completed in $m\times n$ ways.
Now, we will see the number of choices available for the post of principal and vice-principal, when we assign the post from 36 teachers in succession.
Now, if we assign the post of the principal first, then there will be $m=36$ choices available. Then, for the post of vice-principal, there will be $n=36-1=35$ choices available.
Now, from the fundamental principle of multiplication, we can say that the total required number of ways will be equal to $=m\times n=36\times 35=1260$ ways.
Thus, we can appoint one principal and one vice-principal from 36 teachers in a school in $1260$ the number of different ways.

Note:Here, the student should first understand what is asked in the question and then proceed in the right direction to get the correct answer quickly. After that, we should apply the concept of the fundamental principle of multiplication correctly. Moreover, we could have directly used the formula ${}^{n}{{P}_{r}}=\dfrac{n!}{\left( n-r \right)!}$ , with the value of $n=36$ and $r=2$ .