I've no idea what you are trying to argue. I also don't understand your table of situations. In the first move of a Fisher-Yates shuffle, the last element is swapped, so with an initial

    A, B, C
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after the first move we have one of:

    C, B, A
    A, C, B
    A, B, C
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Your table suggests a possible B, C, A after the first move, but you need at least two swaps to go from A, B, C to B, C, A.

Abigail