Professors Adam and Ben each independently pick 20 problems uniformly at random from a set of 100 problems to place on an exam. How many problems do we expect will be picked by both of them? How many problems do we expect will be picked by exactly one of them?

Aschool allots ? 1500 to spend on a trip to the theatre. theatre tickets have a regular cost of ? 55 each and are on offer for 1 5 off. a train ticket for the day will cost ? 12 each. if 2 teachers and the maximum number of students attend, how much money will the school have left over?