A combination lock uses 3 sets of 26 letters of the alphabet in an ordered seque

Question

A combination lock uses 3 sets of 26 letters of the alphabet in an ordered sequence to unlock the lock. (Some examples of an unlocking sequence could be: RZT, XOx, CCc) a) How many different 3 letter sequences are there, if any of the 26 letters can be selected each time? Hint: Any letter can be the 1st AND any letter can be the 2d AND... b) What is the probability that a randomly selected sequence does not have any repeated letters? Hint: The 2nd letter is any letter different from the 1st, AND the 31d is any letter different from the first two. Use the answer from a) to compute the probability as a ratio.

Explanation / Answer

ans a ) there are 26*26*26 = 17576 sequences if any letter can be chosen

ans b) there are 26*25*24 = 15600 sequences with no letter is repeated

P(no letters repeated) =  15600/17576 = 0.8875

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