2nd class combinations

From how many elements you can create 4560 combinations of the second class?

Correct result:

n =  96

Solution:

(n2)=n(n−1)2=4560;n>0 n2−n−9120=0  a=1;b=−1;c=−9120 D=b2−4ac=12−4⋅1⋅(−9120)=36481 D>0  n1,2=−b±D2a=1±364812 n1,2=1±1912 n1,2=0.5±95.5 n1=96 n2=−95   Factored form of the equation:  (n−96)(n+95)=0   n>0⇒n=96{{ n} \choose 2} = \dfrac{n(n-1)}{2}=4560;n>0 \ \\ n^2 -n -9120 =0 \ \\ \ \\ a=1; b=-1; c=-9120 \ \\ D = b^2 - 4ac = 1^2 - 4\cdot 1 \cdot (-9120) = 36481 \ \\ D>0 \ \\ \ \\ n_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 1 \pm \sqrt{ 36481 } }{ 2 } \ \\ n_{1,2} = \dfrac{ 1 \pm 191 }{ 2 } \ \\ n_{1,2} = 0.5 \pm 95.5 \ \\ n_{1} = 96 \ \\ n_{2} = -95 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (n -96) (n +95) = 0 \ \\ \ \\ \ \\ n>0 \Rightarrow n=96

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