Problem 1. Define the sample space of each of the following random experiments. (a) A voter enters a voting booth to vote for one of four presidential candidates, A, B, C, D. (b) A biologist tests an oak tree in the field for the presence of rot. Three routers are tested to see if they're functioning or failed (d) The number of arrivals to a music festival is counted (e) The number of diseased oak trees in a grove of 10 is counted.
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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