A satchel contains fifteen sticks, each of which is individually numbered, 1 through 15. The length of each stick, in inches, equals its number. So, for instance, stick 1 measures 1 inch; stick 2 measures 2 inches, and so forth. You are asked to reach into the bag and randomly select three sticks. What is the probability that you'll withdraw three sticks that would form a Pythagorean right triangle?