Forming a Triangle

The integers from 4 to 9 are placed in a hat. If you draw three numbers, without replacing them, you could form the side lengths of a triangle. Using these three numbers as possible side lengths, determine the probability of forming:

  • an isosceles triangle
  • a scalene triangle
  • a line segment
  • any triangle

How would your answers change if you could replace each of the numbers as you select them? In other words, what would happen to your results if you could put the numbers back into the drawing pool each time they are selected?