Five students are given the following question to answer. "If 13 different types of fruit are available, how many fruit salads could be made using exactly 3 of these fruits?" One at a time, the students show an answer to their teacher in the following order: Student 1 Michelle used 13! to answer the question. 13 to answer the 3 Stan decided to use Student 4 question. Ron suggested using 13 P3 to answer the question. Student 6 Student 7 Jackie answered the question using 13 C10 : 13! would give the correct Kevin thought that Student 9 3! answer.
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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