Permutations And Combinations Question 89

Question: If $ ^{n^{2}-n}C_2{{=}^{n^{2}-n}}C _{10} $ , then $ n= $

Options:

A) 12

B) 4 only

C) $ -3 $ only

D) 4 or $ -3 $

Show Answer

Answer:

Correct Answer: D

Solution:

  • $ ^{n^{2}-n}C_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,\ -3 $ .