SOLUTION: Kelvin is given six sticks. They have lengths 1,2,3,4,5 and 6 feet,respectively. How many distinct can Kelvin form using these sticks one for each side ? (Two triangles are consi

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Question 1075135: Kelvin is given six sticks. They have lengths 1,2,3,4,5 and 6 feet,respectively. How many distinct can Kelvin form using these sticks one for each side ? (Two triangles are considered distinct if they have different side lengths)
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!

In order to form a triangle, the sum of the smaller two 
sides must be greater than the largest side.

There are 7 ways to choose two which form a triangle:

 1.  2, 3, 4     2+3 > 4
 2.  2, 4, 5     2+4 > 5
 3.  2, 5, 6     2+5 > 6
 4.  3, 4, 5     3+4 > 5
 5.  3, 4, 6     3+4 > 6 
 6.  3, 5, 6     3+5 > 6
 7.  4, 5, 6     4+5 > 6

Here are the 13 ways which do not form a triangle
because the sum of the smaller two sides is less 
than or equal to the largest side.

 1.  1, 2, 3     1+2 = 3
 2.  1, 2, 4     1+2 < 4
 3.  1, 2, 5     1+2 < 5 
 4.  1, 2, 6     1+2 < 6
 5.  1, 3, 4     1+3 = 4
 6.  1, 3, 5     1+3 < 5
 7.  1, 3, 6     1+3 < 6
 8.  1, 4, 5     1+4 = 5
 9.  1, 4, 6     1+4 < 6
10.  1, 5, 6     1+5 = 6
11.  2, 3, 5     2+3 = 5
12.  2, 3, 6     2+3 < 6
13.  2, 4, 6     2+4 = 6

Edwin