The gems

The jeweler selects 4 gems for the ring. It has rubies, emeralds and sapphires. How many options does he have?

Correct answer:

x =  15

Step-by-step explanation:

$$\begin{gathered} C_4(6)=\left({\displaystyle \genfrac{}{}{0px}{}{6}{4}}\right)={\displaystyle \frac{6!}{4!(6-4)!}}={\displaystyle \frac{6\cdot 5}{2\cdot 1}}=15 \\ n=3 \\ k=4 \\ x=\left(\genfrac{}{}{0px}{}{n+k-1}{k}\right)=\left(\genfrac{}{}{0px}{}{3+4-1}{4}\right)=15 \end{gathered}$$

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