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# HELELELLEPPPPP

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Dakota randomly selected three different integers 1 through 6. What is the probability that the three numbers selected could be the sides of a triangle? Express your answer as a common fraction.

Sep 23, 2019

$$\text{What's necessary for a triangle is that the}\\ \text{sum of the lengths of any two sides is greater than the length of the third}\\ \text{a little work shows that there are 34 valid unordered triplets that serve as triangle lengths}\\ \text{there are a total of \dbinom{3+6-1}{6-1}=56 total unordered triplets}\\ \text{Thus the probability is p=\dfrac{34}{56} = \dfrac{17}{28}}$$