Question: 2017 Fall Midterm - 1
Let $n \geq 8$ be an even integer and let $S = \{1,2,3,\dots,n\}$. Consider 7-element subsets of $S$
that consist of 4 even numbers and 3 odd numbers. How many such subsets are there?
(a)
${n \choose 4} \cdot {n \choose 3}$
(b)
${n/2 \choose 4} \cdot {n/2 \choose 3}$
(c)
${n/2 \choose 4} + {n/2 \choose 3}$
(d)
${n \choose 4} + {n \choose 3}$