Evaluate 7C6...I did the multiplication and got 5040 and it is marked wrong. What part of the equation are they looking for as an answer?

Question

unklerhaukus · Answer

$$^nC_k=\left(\begin{array}{v}n\k\end{array}\right)=\frac{n!}{k!(n-k)!}$$

unklerhaukus · Answer

A simpler way to look at this problem is to think about what $^nC_k$ means.

$^nC_k$ means we have n options and we  choose k of them to be in the set .

for 0≤k≤n

$^nC_k=^nC_{n-k}$

so it is equivalent to having n options and and choosing n-k to not be in the set