1.Find the value of the factorial. 3​!   2.Find the value of the factorial. 10​!   3. Find the value of the permutation. 8P1   4.Find the value of the permutation. 8P0   5.Find the value of the combination. 5C0   6.A woman has two skirts and ten blouses.Assuming that they all​ match, how many different skirt​-and-blouse combinations can she ​wear?   7.Four members from a 57​-person committee are to be selected randomly to serve as​ chairperson, vice-chairperson,​ secretary, and treasurer. The first person selected is the​ chairperson; the​ second, the​ vice-chairperson; the​ third, the​ secretary; and the​ fourth, the treasurer. How many different leadership structures are​ possible?   8.How many different simple random samples of size 5 can be obtained from a population whose size is 44​?   9.Suppose a shipment of 150 electronic components contains 3 defective components. To determine whether the shipment should be​ accepted, a​ quality-control engineer randomly selects 3 of the components and tests them. If 1 or more of the components is​ defective, the shipment is rejected. What is the probability that the shipment is​ rejected?

Free groceries To attract shoppers, a supermarket runsa weekly contest that involves “scratch-off” cards. Witheach purchase, customers get a card with a black spotobscuring a message. When the spot is scratched away,most of the cards simply say, “Sorry—please try again.” But during the week, 100 customers will get cards thatmake them eligible for a drawing for free groceries. Tenof the cards say they may be worth $200, 10 others say$100, 20 may be worth $50, and the rest could be worth$20. To register those cards, customers write their nameson them and put them in a barrel at the front of the store.At the end of the week the store manager draws cards atrandom, awarding the lucky customers free groceries in the amount specified on their card. The drawings con-tinue until the store has given away more than $500 of free groceries. Estimate the average number of winnerseach week.

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