91Ó°ÊÓ

There are 16 students. Four are to be selected for allotting houses.

The formula of combination is used to estimate the number of ways in which r items can be selected from n items without replacement when the order of the items does not matter.

${}^n{C}_r=\frac{n!}{\left(n-r\right)!r!}$

Let A be the event of selecting the youngest four students.

The total number of ways in which four students can be selected from 16 students (in any order) is computed below:

$$\begin{gathered} {}^{16}{C}_4=\frac{16!}{\left(16-4\right)!4!} \\ =1820 \end{gathered}$$

The number of favorable ways in which the four youngest students can be selected is one.

The probability of selecting the four youngest students is shown below:

$$\begin{gathered} P\left(A\right)=\frac{\text{Number}\text{of}\text{favourable}\text{ways}}{\text{Total}\text{number}\text{of}\text{ways}} \\ =\frac{1}{1820} \end{gathered}$$

Therefore, the probability of selecting the four youngest students is $\frac{1}{1820}$.