# 2nd class variations

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

Result

n =  50

#### Solution:

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

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