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Question
A letter lock contains 3 rings, each ring containing 5 different letters. Determine the maximum number of false trials that can be made before the lock is opened?
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Solution
Since there are 3 rings each containing 5 different letters.
∴ each ring can be adjusted in 5 different ways,
i.e., m = 5, n = 5, p = 5
∴ by the fundamental principle, 3 rings can be arranged in
= m × n × p
= 5 × 5 × 5
= 125 ways
Out of these 125 trials only one trial is successful to open the lock.
Hence, the maximum number of false trials
= 125 − 1
= 124
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