Represented 4324

A bag contains 20 candies in five different flavors: cherry, lemon, orange, mango, and cola. We know that there is at least one of each flavor in the pocket and that there are twice as many lemons as cherry ones. How many ways can different flavors be represented in a bag?

Correct answer:

n =  42504

Step-by-step explanation:

$$\begin{gathered} C_5(24)=\left(\genfrac{}{}{0ex}{}{24}{5}\right)=\frac{24!}{5!(24-5)!}=\frac{24\cdot 23\cdot 22\cdot 21\cdot 20}{5\cdot 4\cdot 3\cdot 2\cdot 1}=42504 \\ n=\left(\genfrac{}{}{0ex}{}{20+5-1}{5}\right)=42504 \end{gathered}$$

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