Question

6.) Alan, Becky, Jesus, and Mariah are four students in the chess club. If two of these students will be selected to represent the school at a national convention, how many combinations of two students are possible? Your answer Please fill out this field.

Answer 1

Let's begin by listing out the information given to us:

There are four students: n = 4

Number of students to be selected: r = 2

To calculate the combination of 2 students to be chosen, we use:

$\begin{gathered} ^4C_2=\frac{n!}{(n-r)!}=\frac{4!}{(4-2)!}=\frac{4!}{2!} \\ ^4C_2=\frac{4\cdot3\cdot2\cdot1}{2\cdot1}=\frac{4\cdot3}{1}=12 \\ ^4C_2=12 \end{gathered}$

Therefore, there 12 possible combinations from these