SOLUTION: Four segments measure 16, 19, 43 and 50 centimeters. What is the probability that a triangle can be formed if three of these segments are chosen at random?

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Question 1043725: Four segments measure 16, 19, 43 and 50 centimeters. What is the probability that a triangle can be formed if three of these segments are chosen at random?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

A scalene triangle can be formed if and only if the two 
shorter sides added together is greater than the longest 
side.  Since 16 and 19 only add to give 35, and the other 
two numbers are greater than that, both 16 and 19 cannot
be sides of the same triangle. So the only way that they 
can form a triangle is to select one of those for the
shortest side and the two largest ones for the other two
sides.

{16,43,50}  or {19,43,50}

But the number of ways to choose any three is

4 numbers Choose 3 = 4C3 = 4

So the probability is 2 ways out of 4 or  2/4 or 1/2.

Edwin