A builder gets bored one day and decides to try constructing a building by taking lengths of the frame material and throwing them in the air. He knows that one type of material will break in three places and the other in two.

One of the rod of frame material of unit length will break randomly¹. It will break in two places. What is the probability that the three pieces thus formed can be assembled into a triangle?

Another type of rod of unit length follows the same distribution but will break in three places. What is the probability that the four pieces can be assembled into a rectangle?

The builder needs 22 triangles and 5 rectangles to construct his building. What is the probability that he will be able to construct this in 100 goes?