SOLUTION: If the 26 letters of the alphabet are arranged at random in a row, what is the probability that the letters A and B are next to each other?

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Question 856069: If the 26 letters of the alphabet are arranged at random in a row, what is the probability that the letters A and B are next to each other?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The number of ways to arrange the 25 things where "AB"
is one thing, and the other letters are the other 24 things, is:

{AB,C,D,E,F,...,X,Y,Z} is 25!

The number of ways to arrange the 25 things where "BA"
is one thing, and the other letters are the other 24 things, is:

{BA,C,D,E,F,...,X,Y,Z} is also 25!

So that 2×25!

out of the number of ways to arrange the 26 things:

{A,B,C,D,E,F,...,X,Y,Z}

which is 26!

Answer: 2%2A25%21%2F26%21 =  =  = 2%2F26 = 1%2F13

Edwin