A large cake is in a room. The first person who comes in takes of the cake. Then a second person takes - of what is left. Then a third person takes - of what is left. And so on. 1. Complete the table for C(n), the fraction of the original cake left after n people take some. 2. Write two definitions for C: one recursive and one 1. non-recursive. C(n) 3. What is a reasonable domain for this function? Be prepared to explain your reasoning. 1 2
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.
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