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 $\times$ 10 $\times$ 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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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?

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