# Triangles

Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle?

Result

n =  7

#### Solution:

$a+b>c \ \\ n_{1}=\dfrac{ 5 \cdot \ 4 \cdot \ 3 }{ 3 \cdot \ 2 }=10 \ \\ \ \\ 5>=2+3 \ \\ 6>=2+3 \ \\ 6>=2+4 \ \\ \ \\ \ \\ n=n_{1}-3=10-3=7$

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