Question

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?

Answer 1

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

Answer 2

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