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?

Result

n =  57

Solution:

C2(7)=(72)=7!2!(7−2)!=7⋅62⋅1=21  n=(72)+5⋅ 7+1=21+5⋅ 7+1=57C_{{ 2}}(7) = \dbinom{ 7}{ 2} = \dfrac{ 7! }{ 2!(7-2)!} = \dfrac{ 7 \cdot 6 } { 2 \cdot 1 } = 21 \ \\ \ \\ n = { { 7 } \choose 2 } + 5 \cdot \ 7 + 1 = 21+ 5 \cdot \ 7 + 1 = 57

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