Chapter 13.9, Problem 3AGP

To determine

The number of ways to select the two students from the following list of students:

Student council candidates
J	E	D
M	Ju	C

Answer to Problem 3AGP

Through the $30$ ways two students can be selected for student council representatives.

Explanation of Solution

Given:

Student council candidates
J	E	D
M	Ju	C

  $\begin{array}{l}n=6\\ r=2\end{array}$

Concept Used:

The formula for combination is given by the following expression:

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

Calculation:

The ways to select two students from six members is calculated as:

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

Put the given data in the above formula:

  $\begin{array}{l}C{}_2=\frac{6!}{\left(6-2\right)!}\\ C{}_2=\frac{6!}{4!}\\ C{}_2=6\times 5\\ C{}_2=30\end{array}$

Conclusion:

Hence, the required number of ways is $C{}_2=30$