Glass with icecream

We have 6 kinds of ice cream and 5 kinds of fruit. We put 3 cups of ice cream and 2 fruits into each glass. How many can unique decorated glasses be?

Correct answer:

n =  200

Step-by-step explanation:

$$\begin{gathered} C_3(6)=\left(\genfrac{}{}{0ex}{}{6}{3}\right)=\frac{6!}{3!(6-3)!}=\frac{6\cdot 5\cdot 4}{3\cdot 2\cdot 1}=20 \\ {C}_2(5)=\left(\genfrac{}{}{0ex}{}{5}{2}\right)=\frac{5!}{2!(5-2)!}=\frac{5\cdot 4}{2\cdot 1}=10 \\ n=\left(\genfrac{}{}{0ex}{}{6}{3}\right)\cdot \left(\genfrac{}{}{0ex}{}{5}{2}\right)=20\cdot 10=200 \end{gathered}$$

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