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Mathematics 21 Online
OpenStudy (anonymous):

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?

OpenStudy (kropot72):

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

OpenStudy (anonymous):

Thank you!

OpenStudy (kropot72):

You're welcome :)

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