1 .
Let $n \geq 8$ be an even integer and let $k$ be an integer with $2 \leq k \leq n/2$. Consider
$k$-element subsets of the set $S = \{1,2,\dots,n\}$. How many such subsets contain at least two even
numbers?
(a)
${n \choose k} - {n/2 \choose k - 1} - \frac{n}{2} \cdot {n/2 \choose k - 1}$
(b)
${n \choose k} - {n/2 \choose k} - \frac{n}{2} \cdot {n/2 \choose k - 1}$
(c)
${n \choose k} - {n/2 \choose k} - \frac{n}{2} \cdot {n/2 \choose k}$
(d)
${n \choose k} - {n/2 \choose k - 1} - \frac{n}{2} \cdot {n/2 \choose k}$