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**Question:**

*"In a lottery game each player tries to guess right 6 numbers designated in advance by choosing randomly from among numbers from 1 to 20. Given that one player guessed right 5 numbers out of 6 that he/she picked, what is the probability of guessing right the 6 numbers?"*

The problem sounds to me an application of Bayes' Theorem, for we know "...one player guessed it right 5 numbers..." However, I couldn't figure out the cardinality of sets to be used in calculation. For instance, when we think of ##S(5)## as the set of 5 numbers guessed right and ##S(6)## as the set of 6 numbers guessed right, what are the cardinalities of ##S(5)## and ##S(6)## (##|S(5)|## and ##|S(6)|##)?