The five finalists in the Miss Universe contest are MissArgentina, Miss Belgium, Miss U.S.A., Miss Japan, andMiss Norway. In how many ways can the judges choose(a) the winner and the first runner-up;(b) the winner, the first runner-up, and the secondrunner-up?
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.
The five finalists in the Miss Universe contest are Miss
Argentina, Miss Belgium, Miss U.S.A., Miss Japan, and
Miss Norway. In how many ways can the judges choose
(a) the winner and the first runner-up;
(b) the winner, the first runner-up, and the second
runner-up?
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