Question: 2018 Fall Midterm - 8
Consider a set $\mathcal{B} = \{B_1,B_2,\dots,B_{13}\}$ of 13 beer bottles and a set
$\mathcal{C} = \{C_1,C_2,\dots,C_{12}\}$ of 12 cider bottles.
Consider subsets $X$ of $\mathcal{B} \cup \mathcal{C}$, such that $X$ consists of exactly 5 beer bottles and all cider bottles in $X$ have an even index.
How many such subsets $X$ are there?
Consider subsets $X$ of $\mathcal{B} \cup \mathcal{C}$, such that $X$ consists of exactly 5 beer bottles and all cider bottles in $X$ have an even index.
How many such subsets $X$ are there?
(a)
None of the above.
(b)
${13 \choose 5} \cdot 2^6$
(c)
${13 \choose 5} \cdot 2^5$
(d)
${12 \choose 5} \cdot 2^6$