If (n^{2} - nC\_{2} =^{n^{2} - n}C\_{10}), then (n =) | MATH - DEFINITON OF COMBINATIONS, CONDITION COMBINATIONS, DIVISION INTO GROUPS, DERANGEMENTS | SolveeIt

If $n^{2} - nC_{2} =^{n^{2} - n}C_{10}$ , then $n =$

4 only

$- 3$ only

4 or $- 3$

Answer

4 or $- 3$

Explanation

$n^{2} - nC_{2} =^{n^{2} - n} ⥂ C_{10} \Rightarrow^{n^{2} - n} ⥂ C_{n^{2} - n - 2} =^{n^{2} - n} ⥂ C_{10}$

$\Rightarrow n^{2} - n - 2 = 10$ or $n = 4,\mspace{6mu} - 3$ .

Question: If \(n^{2} - nC_{2} =^{n^{2} - n}C_{10}\), then \(n =\)...