1 .
You are given 20 beer bottles $B_1,B_2,\dots,B_{20}$ and 30 cider bottles $C_1,C_2,\dots,C_{30}$.
Assume you arrange these 50 bottles on a horizontal line such that
- the leftmost 10 bottles are all beer bottles, and
- the rightmost 10 bottles are all cider bottles.
(a)
${20 \choose 10} \cdot 10! \cdot {30 \choose 10} \cdot 10! \cdot 30!$
(b)
$50!$
(c)
${20 \choose 10} \cdot 10! \cdot {30 \choose 10} \cdot 10!$
(d)
${20 \choose 10} \cdot {30 \choose 10} \cdot 30!$