In a New York daily lottery game a sequence of three digits (not necessarily different) in the range 0-9 are selected at random. Find the probability that two of three of them digits are the same.
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.
In a New York daily lottery game a sequence of three digits (not necessarily different) in the range 0-9 are selected at random. Find the probability that two of three of them digits are the same.
- The range of numbers in the lottery is 0 - 9.
- The total digits in the lottery is 3(not necessarily different).
Here, total number of digits from 0 to 9 is 10.
The number of digits in lottery is 3.
Hence the total number of outcomes is,
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