Pairs Blue
How many different pairs can you make with 85 elements?
For example, say you have 85 different colors. How many different pairs like these:
Red and blue
Blue and yellow
Green and indigo
Yellow and magenta
Can you make?
NOTE: Red and Blue is NOT the same as Blue and Red. Equal pairs (blue and blue) count
Element ONE could be paired with itself, ONE-ONE, and with 84 others for a TOTAL of 85 for that GROUP, the SET starting with a ONE in EACH PAIR.
Your NOTE makes it easier as we will not need to exclude one of the later group's pairs, such as TWO-ONE on account of it being identical with ONE-TWO on the basis that your NOTE says "by definition that TWO-ONE is NOT the same as ONE-TWO."
Therefore, and similarly, there exists 85 possible pairs for each and every subsequent ELEMENT, 84 with others and one with itself. If and only if an element can be paired with its identical element.
IF IT CANNOT because there is only ONE INSTANCE of each element, THEN only 84 pairs are possible for each of the 85 elements.
Therefore, for ONE INSTANCE of each element the ANSWER is 84 times 84 possible pairs.
But if TWO INSTANCES of a particular element are possible, such as ONE-ONE, TWO-TWO, and the like, THEN 85 times 85 pairs are possible.
So I would say the ANSWER to your Q is 85 x 85 possible pairs.
BUT, I am NOT a math head, so this will do if not overruled by a Math Head.
But it does seem to be the logical answer to someone like myself, mostly biology, but some of all other sciences....
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