In ”Bakketivoli” there are 14 restaurants. The management knows that the quality of the restaurants is extremely important for the reputation of the amusement park. It is particularly important for the guests, that the restaurants receive the highest grade from the food authorities’ inspections. The highest grade is shown as a happy smiley on the control reports that all restaurants must display. The management has therefore established their own control system to ensure that restaurants always receive a happy smiley after the food authorities’ inspections. Each month 5 restaurants will be selected, and thoroughly examined for errors in the handling of food. Assume that in a given month there are 3 restaurants that handle their food improperly. Calculate the probability that out of the 5 selected restaurants, none of them handle their food improperly. Solution there are C(14,5) ways to pick 5 restaurants there are C(11,5) ways to picks 5 restaurents from 11 that all handle food properly so P = C(11,5)/C(14, 5) = 11*10*9*8*7 / 14*13*12*11*10 = 3/13.