Challenge Problem :"Pick Up Sticks"

[atharshiraz]

The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability that Tommy CANNOT form a triangle from the 3 sticks?
(A) 11/32
(B) 13/32
(C) 15/32
(D) 17/32
(E) 19/32

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I am getting 3/4 as the solution.

If x and y are the sides of a triangle then the third side z is :
|x-y|< z< x+y

The number of ways that a triangle can be made with sticks that are 1,2,3 and 4 inches are as follows. The only combination that works is 2,3,4.
If we consider the various orders in which the sticks are picked :
2,3,4
2,4,3
3,2,4
3,4,2
4,2,3
4,3,2
= 6 ways that a triangle can be made from the 4 sticks

The total number of ways of picking 3 sticks out of 4 are:
4x3x2 = 24

That is (6/24) chance that a triangle can be made.

So the probability that a triangle can NOT be made is
1-(6/24) = 18/24 =3/4.

I don't see the answer 3/4 up there so I must be doing something wrong.

[atharshiraz]

ugh sorry I cannot believe I didn't read the question properly. Ok, I figured out why I was getting the wrong answer. It is very odd that I did not understand the question after reading it several times that was not even under exam pressure.

[jnelson0612]

ugh sorry I cannot believe I didn't read the question properly. Ok, I figured out why I was getting the wrong answer. It is very odd that I did not understand the question after reading it several times that was not even under exam pressure.

Glad that you figured it out . . . what you describe has happened to me many times. :-)