For this problem, assume Gwen and Harry have 5 types of cones and 11 flavors of ice cream. (1) In how many different ways can your order one cone and two scoops of ice cream? (As in the book, putting one flavor on top of another is different from putting them the other way around.) (2) In how many different ways can your order one cone and two scoops of ice cream which are not the same flavor?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
For this problem, assume Gwen and Harry have 5 types of cones and 11 flavors of ice cream.
(1) In how many different ways can your order one cone and two scoops of ice cream? (As in the book, putting one flavor on top of another is different from putting them the other way around.)
(2) In how many different ways can your order one cone and two scoops of ice cream which are not the same flavor?
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