An ice cream shop sells 30 kinds of ice cream and 3 different kinds of cones. How many ways can a dozen two scoop ice cream cones by ordered if the ice cream cones must differ by at least one flavour or cone type?
The number of combinations of different kinds of ice cream taken two at a time is 30C2. Each of these combinations can be taken with one of the three kinds of cone, giving a total number of combinations with different kinds of ice cream and different kinds of cone as follows: 30C2 * 3 = 1305 The number of combinations of two scoops of the same kind of ice cream with each type of cone is 30 * 3 = 90 Therefore the total number of combinations meeting the specification is given by 1305 + 90 = 1395 The number of ways of ordering two scoop ice creams from the 1395 different combinations is therefore 1395C12
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