Math Problem Solver

\(\operatorname{C}(4, 0) = 1\)

$$\begin{aligned} \operatorname{C}(4, 0)&=\frac{4!}{0! \left(0 + 4\right)!}\ \ \ \small{\color{grey}\text{using the formula} \operatorname{C}(n, k) = \frac{n!}{k!(n-k)!}}\\&=\frac{1}{0!}\\&=1^{-1}\\&= 1 \end{aligned}$$

\(\operatorname{C}(n, k)\), also written as \(nCk\) or \(n \choose k\), is the combination function. It is often referred to as 'n choose k.' The combination function can be written in factorial form as\(\operatorname{C}(n, k) = \frac{n!}{k!(n-k)!}\)