SOLUTION: A 3 character key code is randomly generated by a computer using the 26 letters of the alphabet and the 10 digits 0-9. The letters and numbers can be used more than once. What is t

Question 939219: A 3 character key code is randomly generated by a computer using the 26 letters of the alphabet and the 10 digits 0-9. The letters and numbers can be used more than once. What is the probability that the 3 characters in a key code, listed as they are randomly generated, will spell the world ADD?
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

There are 26 letters and 10 digits for a total of 36 character choices for each of the three positions, assuming upper- and lower-case letters are considered identical.

Given that the choice of characters is random, by the multiplication rule, there is a total of possible ways to generate a 3-character code, out of which ADD is one.

The three letters required to spell ADD are {A,D,D}, and they can be generated in three different orders: ADD,DAD and DDA. Thus the probability of generated theses characters is

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