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?
Given: Each ring consists of 10 letters and there are three rings. Only one code is correct which will open the lock.
Therefore one subtracted from total possible outcomes will give the number of unsuccessful attempts.
At a time only one letter can appear in each ring
So total number of possible outcomes are 10C1 × 10C1 × 10C1 = 1000
Hence, the number of unsuccessful attempts to open the lock is 1000 - 1 = 999