Question: 2017 Fall Final - 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.

How many such arrangements are there? (The order of the bottles matters.)