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:

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

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