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

Guest Mar 14, 2015

#2**+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

#1**+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.

Melody
Mar 15, 2015

#2**+10 **

Best Answer

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