Suppose there are 5 sections (A, B, C, D, and E) in the Final Exam Question (STA 201, summer 2020). A student can either pass or fail in a section. One student will pass the exam only if s/he passes in all 5 sections. a. In how many ways can a student fail in exactly one section of the final test? b. In how many ways can a student pass exactly 3 of those 5 sections? c. In how many can a student fail to pass the final exam? d. Knowing that a student has equal chance to pass or fail in a section, determine the probability of a student passing the final test?
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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