Exercise 5 Suppose there are n students in this class. We are interested in the probability of the event A that at least two students have the same birthday. For simplicity, we assume that no student was born on February 29 and that all students were born independently of each other (no twins!). We also assume that each day in the year is equally probable for a birthday. (a) The instructor asks all students for their birthdays. How many possible outcomes are there? (b) Describe in words what A' means. (c) Compute P(A') in dependence of n.

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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.