Triangle probability

We have the numbers 4, 6, 8, 10, and 12. What is the probability that with a randomly selected triangle, these will be the lengths of the sides of a scalene triangle?

Final Answer:

p =  0.7

Step-by-step explanation:

$$\begin{gathered} C_3(5)=\left(\genfrac{}{}{0ex}{}{5}{3}\right)=\frac{5!}{3!(5-3)!}=\frac{5\cdot 4}{2\cdot 1}=10 \\ n=\left(\genfrac{}{}{0ex}{}{5}{3}\right)=10 \\ 4+6\le 10 \\ 4+6\le 12 \\ 4+8\le 12 \\ p=1-3/n=1-3/10=0.7 \end{gathered}$$

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