Question

 If  ⁿC₈ = ⁿC₂, find ⁿC_2.

Answer 1

_{It is known that,}\(^nC_a= \space^nC_b\)
\(⇒a=b\space or\space  n=a+b\)
_Therefore\(,^nC_8\space =\space ^nC_2\)
\(⇒n=8+2=10\)
\(∴ ^nC_2=\space^{10}C_2=\frac{10}{2!\left(10-2\right)!}\)
\(=\frac{10!}{2!8!}=\frac{10\times9\times8!}{2\times1\times8!}=45\)