a job, he must immediately decide whether to accept it or decline it and consider the He becomes available. Notice that when considering a new job offer, Joe only knows the relative rank of that job compared to the ones he has already declined. Assume that all n! orderings are equally likely and that once a job is declined it is gone forever. Suppose Joe's strategy is to reject the first k jobs and then accept the first one that is better than all of those first k. For a given value of k, what is the probability that Joe selects the best job? Ii morimize the probability that Joe selects the best job under this strategy?
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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