Probability letter different

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Problem: John, Harry, and Steve wrote down A, B, and C secretly. What is the probability that Harry's letter will be different from both John and Steve's letter?


Solution: Total number of events = (aaa, bbb, ccc, abc, aab, aac, bba, bbc, cca, ccb)= 10

Total events when at least one has different letter (abc, aab, aac, bba, bbc, cca, ccb)= 7

P(Total events when at least one has different letter) = Total events when at least one has different letter / total number of events = 7/10

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