The different two-letter initials can people have using the upper case characters in the English alphabet is 676 (if no specifications are given)
The question has not specified other conditions so we have assumed it by cases and solved it
Case 1 -
“Everything” allowed, means that we are considering solutions like “AA” and “BA, AB”
If this is the case then there are => 26 x 26 = 676 Combinations,
Case 2-
No repetition allowed
Here, we are excluding cases like “AA, BB” etc so here we have
26 x 25 = 650 as our answer
Case 3-
no repetition allowed + unique set every time, So
here we will have ²⁶C₂ (this is basic combinatorics formula )
= (26 x 25)/2
= 325 combinations possible
Case 4 -
Repetition allowed + unique set every time
here we will assume along with the uniqueness of each combination we will add Repeated combinations, Here we have “AA, BB, CC,……..ZZ” 26 new combinations along with unique ones So,
²⁶C₂+ 26 = 325 + 26 = 391 possible cases.
and I would recommend adding more detail to your question specifying the conditions in a better way, but the technically correct answer to your questions if no conditions are CASE 1.
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