Question

Variables in Combinations? How would I turn C(x, 10) into an algebraic expression?

Answer 1

\[_nC_k=\frac{n!}{k!(n-k)!}\] so
\[_xC_{10}=\frac{x!}{10!(x-10)!}\]

Answer 2

^^ can also be further reduced.
\[x!=x(x-1)(x-2)\cdots(x-10)!\]
so
\[{}_xC_{10}=\frac{x!}{10!(x-10)!}=\frac{x(x-1)(x-2)\cdots(x-10)!}{10!(x-10)!}=\frac{x(x-1)(x-2)\cdots(x-9)}{10!}\]

Answer 3

It can actually be found a different way.... I figured it out