# 2nd class variations

From how many elements you can create 2450 variations of the second class?

Result

n =  50

#### Solution:

$V_{ 2 }(n)=2450 \ \\ n * (n-1)=2450 \ \\ \ \\ n \cdot \ (n-1)=2450 \ \\ n^2 -n -2450=0 \ \\ \ \\ a=1; b=-1; c=-2450 \ \\ D=b^2 - 4ac=1^2 - 4\cdot 1 \cdot (-2450)=9801 \ \\ D>0 \ \\ \ \\ n_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 1 \pm \sqrt{ 9801 } }{ 2 } \ \\ n_{1,2}=\dfrac{ 1 \pm 99 }{ 2 } \ \\ n_{1,2}=0.5 \pm 49.5 \ \\ n_{1}=50 \ \\ n_{2}=-49 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (n -50) (n +49)=0 \ \\ \ \\ n>0 \ \\ n=n_{1}=50$

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