Lesson: Introduction to Combinations

You are correct.
Two teams are required to play a game, and the order in which we select the 2 teams does not matter.
So the question can be rewarded as, "In how many different ways can we select 2 teams from 8 teams?
The answer: 8C2

Here's another (non-combinations) way to answer that same question: https://gmatclub.com/forum/there-are-8-teams-in-a-certain-league-and-eac...

Sorry, none of these are correct.

#1) If repeated letters are NOT allowed, then the correct answer is 2 * 25 * 24.
For the first position, select EITHER X or Q (2 options)
For the second position, select any letter EXCEPT the first selected letter (25 options)
For the third position, select any letter EXCEPT the first and second selected letters (24 options)
For example, XQR would be an acceptable word.

If repeated letters ARE allowed, then the correct answer is 2 * 26 * 26.
For the first position, select EITHER X or Q (2 options)
For the second position, select ANY letter (26 options)
For the third position, select ANY letter (26 options)

#2) Your answer of 26C3 is not correct, since the order in which we arrange the letters matters.
The correct answer here is 26 * 26 * 26
For the first position, select ANY letter (26 options)
For the second position, select ANY letter (26 options)
For the third position, select ANY letter (26 options)

#3) Your answer of 26C3 / 26! is not correct, since the order in which we arrange the letters matters.
The correct answer here is 26 * 25 * 24
For the first position, select ANY letter (26 options)
For the second position, select any letter EXCEPT the first selected letter (25 options)
For the third position, select any letter EXCEPT the first and second selected letters (24 options)