Suppose you had five sticks of length 1, 2, 3, 4, and 5 inches. If you chose three at random, what is the likelihood tht the three sticks could be put together, tip to tip, so as to form a triangle?

Now suppose you had twenty sticks, of lengths 1 through 20 inches. If you picked three at random, what is the likelihood that the three could be put together, tip to tip, to form a right triangle?

*(Assume that a triangle has to have some area)*

(In reply to

re: Quick partial answer by Charlie)

2, 3, and 4

2, 3, and 5

3, 4, and 5

all produce triangles...

There are 5x4x3 = 60 different *Ordered* possibilities.

Taken 3 at a time (6 orderings each...) leaves 10 distinct possibilities

For completion, the 7 distinct orderings that DON'T produce triangles are:

1, 2, 3

1, 2, 4

1, 2, 5

1, 3, 4

1, 3, 5

1, 4, 5

2, 3, 5

So, Charlie is correct **3/10 = .3**