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Seven sticks with lengths 2, 3, 5, 7, 11, 13 and 17 inches are placed in a box. Three of the sticks are randomly selected. What is the probability that a triangle can be formed by joining the endpoints of the sticks? Express your answer as a common fraction.

 Dec 30, 2018
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Seven sticks with lengths 2, 3, 5, 7, 11, 13 and 17 inches are placed in a box. Three of the sticks are randomly selected. What is the probability that a triangle can be formed by joining the endpoints of the sticks? Express your answer as a common fraction.

 

17,13,        and 5 or 7 or 11         (3)

17, 11,       and 7                          (1)

 

13, 11,       and  3,5,7                  (3)

13, 7,         and    none

 

11, 7           and 5                        (1)

7, 5,           and 3                        (1)

5, 3,           and none

 

equals  9  favourable outcomes   (you need to check)

 

Can you see how I have done this?  What needs to happen for three lengths be able to form a triangle?

 

7C3=35

 

Probability = 9/35

 Dec 30, 2018
edited by Melody  Dec 30, 2018

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