Fernando's Frames offers a low-cost, do-it-yourself picture-framing option. To save money, you determine the shape of the frame and select and purchase the side pieces. Side pieces of various lengths are available. Corner fittings are free. Fernando helps you assemble the frame.
One day, Fernando's friend Fred came into the frame shop. He asked for six side pieces, 2, 3, 4, 5, 6, and 7 inches long. He said he could take any three of those side pieces and make a triangular frame.
"Don't be so sure of that!" said Fernando.
What is the probability that any three of these side pieces will form a triangular frame?