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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 22, 2018
 #1
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(2, 3, 5, 7, 11, 13, 17 )

 

We have 35 possible sets

 

(2,3,5) (2,3,7) (2,3,11) (2,3,13) (2,3, 17)

(2, 5, 7) (2, 5,11) (2, 5, 13) (2,5, 17)

(2, 7,11) (2, 7, 13) (2, 7, 17)

(2, 11,13) (2,11, 17)

(2,13, 17)                            

 

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

(3, 7, 11) (3, 7, 13) (3, 7, 17)

(3, 11, 13,) (3, 11, 17)

(3, 13, 17)                        

 

(5, 7, 11) (5, 7, 13) (5, 7, 17)

(5, 11, 13) (5, 11, 17)

(5, 13, 17)   

 

(7, 11, 13)  (7, 11, 17)

(7, 13, 17)

(11,13, 17)

 

 

By the Triangle Inequality....Only 9  are possible

 

So    9 / 35   

 

 

 

cool cool cool

     

 Dec 22, 2018

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