This question generalizes the example of "evil-doers" visiting hotels, as in section 1.2.3. suppose as before that there are a billion people being monitored for 1000 days. each person has a 1% probability of visiting a hotel on any given day, and hotels hold 100 people each, so there are 100,000 hotels. however, our test for evil-doers is different. we consider a group of p people evil-doers if they all stayed at the same hotel on d different days. derive the formula for the expected number of sets of p people that will be suspected of evil-doing ("false accusations"), assuming that in fact there are no evil-doers, but all people behave at random, following the conditions stated in this problem (1% probability of visiting a hotel, etc.). then, find in the list below, the choice that is the best approximation to the correct value for some d and p. note: you may assume that d and p are sufficiently small that (1000 choose d) can be approximated as 1000d/d!, and similarly for p. we are looking for the choice that is the best approximation to the expected value for the given d and p.