SOLUTION: A restaurant offers its customers a choice of three side dishes with each meal the side dishes can be chosen from a list of 15 possibilities with duplications allowed for instance

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Question 1137399: A restaurant offers its customers a choice of three side dishes with each meal the side dishes can be chosen from a list of 15 possibilities with duplications allowed for instance a customer can order two sides of mashed potatoes and one side of string beans show that there are 680 possible options for the three side dishes
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


He can choose 3 different side dishes the number of ways he can do that is 15 choose 3 = (15*14*13)/(3*2*1) = 455 or he can choose 2 of one side dish and 1 of another the number of ways he can choose 2 of the 15 side dishes is 15 choose 2 = (15*14)/(2*1) = 105 but in those cases either one of the 2 he chooses could be the one he gets 2 of so the number of possibilities there is 2*105 = 210 or finally he could choose 3 of a single side dish and the number of ways of doing that is 15 choose 1 = 15 so the total number of possibilities is 455+210+15 = 680.

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