Triangle Side Lengths Probability

We have the numbers 4, 6, 9, 13, and 15. What is the probability that these will be the lengths of the sides of the triangle?
(Consider only scalene triangles.)

Final Answer:

p =  0.6

Step-by-step explanation:

$$\begin{gathered} C_3(5)=\left(\genfrac{}{}{0ex}{}{5}{3}\right)=\frac{5!}{3!(5-3)!}=\frac{5\cdot 4}{2\cdot 1}=10 \\ n=\left(\genfrac{}{}{0ex}{}{5}{3}\right)=10 \\ 4+6{\le }_{13} \\ 4+6{\le }_{15} \\ 4+9{\le }_{13} \\ 6+9{\le }_{15} \\ p=1-4/n=1-4/10=0.6 \end{gathered}$$

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