11!/(3!3!2!2!) = 39916800/144 = 277200
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There are 12 two letter arrangements of the letters in PARK.
There are 172 different arrangements.
Infinitely many. You could, for example, cut out images of the 8 letters and paste then on the wall facing you. Each letter can take infinitely many positions on that wall so you have infinitely many arrangements.
There are 6! = 720 different arrangements.
Assuming you don't repeat letters:* 7 options for the first letter * 6 options for the second letter * 5 options for the third letter * 4 options for the fourth letter (Multiply all of the above together.)