5.084 Each of the ten radio operators at point A is trying to establish contact with each of the twenty radio operators at point B. How many different variants of such contact are possible?
Solution. The number of pairs containing one radio operator from each point is $10 \times 20=200$. Since for each pair there are only 2 communication options (either communication exists or it does not), there are a total of $2^{200}$ such options.

Answer: $2^{200}$