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Question
In a lottery, a person chooses six different numbers at random from 1 to 20, and if these six numbers match with six number already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game?
Solution
Total number of ways in which one can choose six different numbers from 1 to 20 = 20C6
∴ Total number of elementary events = 20C6 = 38760
Hence, there are 38760 combinations of 6 numbers.
Out of these combinations, one is already fixed by the lottery committee.
Favourable number of elementary events = 1
∴ Required probability = \[\frac{1}{38760}\]
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