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# 02_04ans - STAT 400 Examples for order of the selection is...

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STAT 400 Examples for 02/04/2010 Spring 2011 order of the selection is important order of the selection is not important repetitions allowed (w/ replacement) n r n + r 1 C r repetitions not allowed (w/o replacement) n P r = ( ) ! ! r n n - n C r = ( ) ! ! ! r n r n - 7. The Baskin-Robbins Ice Cream Stores have 31 flavors of ice cream. a) How many different 3-scoop ice cream cones are possible if you are allowed to repeat flavors and want the scoops put on the cone in a particular order? w/ replacement order of the selection is important 31 3 = 29,791 . OR 31 31 31 = 29,791 . 1st 2nd 3rd b) How many different 3-scoop ice cream cones are possible if each scoop is a different flavor and you want the scoops put on the cone in a particular order? w/o replacement order of the selection is important 31 P 3 = ! ! 28 31 = 26,970 . OR 31 30 29 = 26,970 . 1st 2nd 3rd c) How many different 3-scoop cones are possible if each scoop is a different flavor and you don’t care about their order on the cone? w/o replacement order of the selection is not important 31 C 3 = ! ! ! 28 3 31 3 31 = = 4,495 . d) How many different 3-scoop ice cream cones are possible if you are allowed to repeat flavors, but the order in which the scoops are placed into the cone is not important?

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