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?

Correct result:

n =  7

Solution:

$$\begin{gathered} a+b>c \\ {n}_1={\displaystyle \frac{5\cdot 4\cdot 3}{3\cdot 2}}=10 \\ 5>=2+3 \\ 6>=2+3 \\ 6>=2+4 \\ n=n_1-3=10-3=7 \end{gathered}$$

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