Points in space

There are n points, of which no three lie on one line and no four lies on one plane. How many planes can be guided by these points? How many planes are there if there are five times more than the given points?

Correct answer:

r =  10
r2 =  35

Step-by-step explanation:

C3(10)=(310)=3!(103)!10!=3211098=120 n=10  r=(3n)=120=10
C3(7)=(37)=3!(73)!7!=321765=35 5n=(3n) 5n=n /3 5n=n(n1)(n2)(n3) /3  5=(x1)(x2)/6  0.166667x2+0.5x+4.667=0 0.166667x20.5x4.667=0  a=0.166667;b=0.5;c=4.667 D=b24ac=0.5240.166667(4.667)=3.3611173333 D>0  x1,2=2ab±D=0.3333340.5±3.36 x1,2=1.499997±5.4999940909186 x1=6.9999910909246 x2=3.9999970909126   Factored form of the equation:  0.166667(x6.9999910909246)(x+3.9999970909126)=0  r2=(3x1)=35

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