Solve the problem
There are 6 finalist in a singing competition. If a person guesses randomly the top three winners (in any order), what is the probability that they will guess correctly?
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To solve this problem, we need to find the probability of guessing all three winners correctly.
Since there are 6 finalists, there are 6 choices for the first winner, 5 choices for the second winner (as one finalist has already been chosen), and 4 choices for the third winner (as two finalists have already been chosen).
Therefore, the total number of possible outcomes is 6 * 5 * 4 = 120.
Since there are only 3 winners, there are also 3! = 6 possible orders in which they can be chosen.
Therefore, the probability of guessing all three winners correctly is 6/120 = 1/20.
Thus, the probability that the person will guess correctly is 1/20 or 0.05 (5%).