Question

La Michoacana has 4 flavors of icecream: mint,chocolate, strawberry, and vanilla. You can have twoscoops. How many unique variations you can create?

Answer 1

To calculate the possible combinations we use the following equation:

$\begin{gathered} nC_r=\frac{n!}{r!\cdot(n-r)!} \\ n=4 \\ r=2 \\ \end{gathered}$$\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}$

So the answer is 6 variations you can create with 4 flavors of ice cream and only two scoops of unique combinations.