Points in plane

The plane is given 12 points, 5 of which is located on a straight line. How many different lines could by draw from this points?

Correct answer:

n =  57

Step-by-step explanation:

$$\begin{gathered} C_2(7)=\left({\displaystyle \genfrac{}{}{0px}{}{7}{2}}\right)={\displaystyle \frac{7!}{2!(7-2)!}}={\displaystyle \frac{7\cdot 6}{2\cdot 1}}=21 \\ n=\left(\genfrac{}{}{0px}{}{7}{2}\right)+5\cdot 7+1=21+5\cdot 7+1=57 \end{gathered}$$

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