Twelve flowers

A florist has roses, tulips, daffodils, and carnations to use in flower arrangements. If she were to make an arrangement using 12 flowers, how many different combinations of these four types of flowers would be possible?

Correct answer:

x =  455

Step-by-step explanation:

$$\begin{gathered} C_{12}(15)=\left(\genfrac{}{}{0ex}{}{15}{12}\right)=\frac{15!}{12!(15-12)!}=\frac{15\cdot 14\cdot 13}{3\cdot 2\cdot 1}=455 \\ n=4 \\ k=12 \\ m=n+k-1=4+12-1=15 \\ x=\left(\genfrac{}{}{0ex}{}{m}{k}\right)=455 \end{gathered}$$

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