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=(n!)/(r!\cdot(n-r)!) \\ n=4 \\ r=2 \\ \end{gathered}`
`\begin{gathered} nC_r=(4!)/(2!\cdot(4-2)!) \\ nC_r=(1\cdot2\cdot3\cdot3)/(1\cdot2\cdot(2)!) \\ nC_r=(24)/(2\cdot(1\cdot2)) \\ nC_r=(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.