A certain lottery consists of selecting five different numbered balls from numbered 1 to 13 white balls and one from 1 to 14 gold Mega balls. A player wins the jackpot by matching all five numbers drawn from white balls (1 through 13) and matching the number on the gold Mega Ball (1 through 14). A player wins a minimum award of $150 by correctly matching three numbers drawn from white balls (1 through 13) and matching the number on the gold Mega Ball (1 through 14). What is the probability of winning this consolation prize?
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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