A new vaccine is being tested on a group of 4000 people by giving 2500 people the vaccine and the rest a placebo (fake). (a) In how many ways can the 2500 people be selected? (b) Suppose 1800 of the people are over 50.  In how many ways can the 2500 be selected if 1000 must be over 50? (c) Suppose of the 2500 people selected, 800 are to get 2 doses and 1700 are to get 1 dose.  In how many ways can the assignment of 2 doses, 1 dose, and placebo be made?

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