Glass with icecream

We have six kinds of ice cream and five kinds of fruit. If we put three cups of ice cream and two fruits into each glass, how many uniquely decorated glasses can there 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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