Ball Mart has $10^7$ different items in stock across all its stores worldwide. The company has collected billing data for $10^{10}$ customer transactions. Each individual bill has at most $10$ distinct items in it. Ball Mart’s CEO wants to optimize the company’s inventory and has asked for a list of those items that appear in at least $2 \%$ of the billed transactions. Which of the following is the most precise upper bound one can compute for the number of such items, given the data?
- $500$
- $1000$
- $5000$
- $20000$
