Toplay the lottery in a certain state, a person has to correctly select 5 out of 45 numbers, paying $1 for each five-number selection. If 5 numbers picked are the same as the ones drawn by the lottery, an enormous sum of money is bestowed. What is the probabilty that a person with one combination of five number will win? What is the probabilty of winning if 100 different lotery tickets are purchased?
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.
Toplay the lottery in a certain state, a person has to correctly select 5 out of 45 numbers, paying $1 for each five-number selection. If 5 numbers picked are the same as the ones drawn by the lottery, an enormous sum of money is bestowed. What is the probabilty that a person with one combination of five number will win? What is the probabilty of winning if 100 different lotery tickets are purchased?
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