2nd class combinations

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

Correct answer:

n =  96

Step-by-step explanation:

$$\begin{gathered} \left(\genfrac{}{}{0px}{}{n}{2}\right)={\displaystyle \frac{n(n-1)}{2}}=4560;n>0 \\ {n}^2-n-9120=0 \\ a=1;b=-1;c=-9120 \\ D=b^2-4ac=1^2-4\cdot 1\cdot (-9120)=36481 \\ D>0 \\ {n}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{1\pm \sqrt{36481}}{2}} \\ {n}_{1,2}={\displaystyle \frac{1\pm 191}{2}} \\ {n}_{1,2}=0.5\pm 95.5 \\ {n}_1=96 \\ {n}_2=-95 \\ \text{ Factored form of the equation: } \\ (n-96)(n+95)=0 \\ n>0\Rightarrow n=96 \end{gathered}$$

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