Chapter 13, Problem 15SGR

To determine

If 4 students are randomly chosen among 32 students then in how many ways it can be done.

Answer to Problem 15SGR

It can be done in $35960$ ways.

Explanation of Solution

Given information: For an academic challenge team 4 students are randomly chosen for an academic challenge team from 32 students.

Calculation: Since 4 students are chosen from 32 students, therefore it is the case of selection of 4 students among 32 students. Therefore it can be done in $C{}_4$ ways. Therefore,

  $\begin{array}{c}C{}_4=\frac{32!}{\left(32-4\right)!\left(4!\right)}\\ =\frac{32!}{\left(28!\right)\left(4!\right)}\\ =35960\end{array}$

Hence it can be done in $35960$ ways.