Mega Millions is a multi-state lottery played in most U.S. states.As of this writing, the top cash prize was $656 million, going to three lucky winners in three states. Players pick five different numbers from 1 to 56 and one number from 1 to 46.Use this information to solve:A player wins the jackpot by matching all five numbers drawn from white balls (1 through 56) and matching the number on the gold Mega Ball® (1 through 46). What is the probability of winning the jackpot?Express all probabilities as fractions.
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.
Mega Millions is a multi-state lottery played in most U.S. states.As of this writing, the top cash prize was $656 million, going to three lucky winners in three states. Players pick five different numbers from 1 to 56 and one number from 1 to 46.Use this information to solve:A player wins the jackpot by matching all five numbers drawn from white balls (1 through 56) and matching the number on the gold Mega Ball® (1 through 46). What is the probability of winning the jackpot?Express all probabilities as fractions.
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