Probability 7991

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.)

Correct 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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