A family is trying to decide whether to go to Chicago​ (C), Nashville​ (N), or Ocean City​ (O) on their summer vacation. The two​ parents, four ​children, and three grandparents rank their three choices according to the following preference table. Determine the winner using the pairwise comparison method.   Number of Votes 3 2 1 2 1   First Choice C O C N O   Second Choice N C O O N   Third Choice O N N C C   Choose the correct answer below.     A. ​(N) Nashville   B. ​(C) Chicago   C. ​(O) Ocean City   D. There is no winner. There is a tie between Chicago and Nashville.   E. There is no winner. There is a​ three-way tie.

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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.