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How many ways can you write two different letters, so that they are in alphabetical order? For example, AB and CT count, but ZA does not.?

 May 1, 2020
 #1
avatar+657 
+2

We can also note that to form a sequence with two different letters in alphabetical order, we need first pick the letters we'll use, then put them in order. We can choose two letters to use in \($\binom{26}{2} = 325$\) ways, and there's only 1 way to put each pair in order.


Hence, there are 325 sequences that fit the problem.

 

coolsmileycool

 May 1, 2020
 #2
avatar+8958 
+1

I'm guessing...

 

A followed by any other letter is a valid possibility. B followed by any letter except A or B is a valid possibility.

 

With A there are 25 possibilities, with B there are 24 possibilities, with C there are 23, etc.

 

25 + 24 + 23 + 22 + 21 + . . . + 3 + 2 + 1   =   (1/2)(25)(25 + 1)   =   325   laugh

 May 1, 2020

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