Question

A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?

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Solution

Number of ways of marking each of the ring = 10 different letters ∴ Total number of ways of marking any letter on these three rings = 10$×$10$×$10 = 1000 Out of these 1000 combinations of the lock, 1 combination will be successful. ∴ Total number of unsuccessful attempts = 1000 $-$1 = 999

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