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Assume that a dentist has 8 appointments per day and that each appointment time is equally desireable from the perspective of the patient.

Assume that 3 dentists working together as a group each have appointments via the traditional call and book method averaging 6 of the 8 daily appointment slots. In other words, some days they have more or less than 6 bookings but in the aggregrate they each have 6 bookings per day.

Then using a web based (last-minute/day-before) self-booking system where a prospective client picks 3 preferred time slots what is the probability that one of those 3 time slots would be available with at least 1 dentist? With 2 dentists? How can one solve this and similar problems?

Thanks,

Bernie