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 5, 6, Pick Up Sticks (Posted on 2003-11-05)
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)

 See The Solution Submitted by DJ Rating: 3.8571 (7 votes)

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 re(2): Quick partial answer | Comment 3 of 13 |

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
 Posted by SilverKnight on 2003-11-05 14:52:49

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