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# How many 2-letter "words" consist of two different letters arranged in alphabetical order? (Any two letters together is considered a "word."

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652
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How many 2-letter "words" consist of two different letters arranged in alphabetical order? (Any two letters together is considered a "word.")

Mar 14, 2015

#2
+94237
+10

Notice that "a" could come first and be matched with 25 letters  {the rest of them} for a total of 25 words

'b' could come first and be matched with 24 letters for a total of 24 words

"c" could come first and be matched with 23 lettters for a total of 23 words

etc........

So....this appears to just be the sum of the first 25 integers = [26 * 25] / 2  = 325

Hey....Melody and I agree on something!!!

Mar 15, 2015

#1
+94976
+10

any earlier letter then z

any earlier letter then y

----

ab

25*1+24*1+23*1 +    .....  +2*1+1

25+24+23+22+     +1

1+2+3+.......+25

this is an AP

a=1  d=1   n=25

Sn=(n/2) (a+L)

S_25 = 12.5(1+25)=12.5*26 = 325

I think that there are 325 possibilities.

Mar 15, 2015
#2
+94237
+10

Notice that "a" could come first and be matched with 25 letters  {the rest of them} for a total of 25 words

'b' could come first and be matched with 24 letters for a total of 24 words

"c" could come first and be matched with 23 lettters for a total of 23 words

etc........

So....this appears to just be the sum of the first 25 integers = [26 * 25] / 2  = 325

Hey....Melody and I agree on something!!!

CPhill Mar 15, 2015