To calculate the possible combinations we use the following equation:
[tex]\begin{gathered} nC_r=\frac{n!}{r!\cdot(n-r)!} \\ n=4 \\ r=2 \\ \end{gathered}[/tex][tex]\begin{gathered} nC_r=\frac{4!}{2!\cdot(4-2)!} \\ nC_r=\frac{1\cdot2\cdot3\cdot3}{1\cdot2\cdot(2)!} \\ nC_r=\frac{24}{2\cdot(1\cdot2)} \\ nC_r=\frac{24}{4} \\ nC_r=6 \end{gathered}[/tex]So the answer is 6 variations you can create with 4 flavors of ice cream and only two scoops of unique combinations.
