Question: 2019 Fall Midterm - 3
Let $k$ and $n$ be integers with $2 \leq k \leq n$ and consider the set $S = \{1,2,...,n\}$.
What is the number of $k$-element subsets of $S$ that do not contain 1 or do not contain 2?
(a)
${n \choose k} - {n - 2 \choose k - 2}$
(b)
${n - 1 \choose k} + {n - 1 \choose k}$
(c)
${n \choose k} - {n - 1 \choose k - 1} - {n - 1 \choose k - 1}$
(d)
${n - 2 \choose k}$