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There is only one combination and that is AABBCC.

There are 90 permutations. Some of these are:

AABBCC, AABCBC, AABCCB, AACBBC, AACBCB, AACCBB,

ABABCC, ABACBC, ABACCB, ABBACC, ABBCAC, ABBCCA,

ABCABC, ABCACB, ABCBAC, ABCACB, ABCCAB, ABCCBA, etc.

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