Question: 2018 Winter Midterm - 8
Let $m \geq 34$ be an even integer, let $n \geq 1$ be an integer, and consider the two sets
$$
A = \{1,2,\dots,m\}
$$
and
$$
B = \{m+1,m+2,\dots,m+n\}.
$$
Let $k$ be an integer with $17 \leq k \leq n+17$.
Consider subsets $X$ of $A \cup B$, such that $|X| = k, |X \cap A| = 17$, and all elements of $X \cap A$ are even.
How many such subsets $X$ are there?
Consider subsets $X$ of $A \cup B$, such that $|X| = k, |X \cap A| = 17$, and all elements of $X \cap A$ are even.
How many such subsets $X$ are there?
(a)
${m/2 \choose 17} \cdot {n \choose k-17}$
(b)
${m+n \choose 17} \cdot {n \choose k-17}$
(c)
${m \choose 17} \cdot {n \choose k-17}$
(d)
${m/2+n \choose 17} \cdot {n \choose k-17}$