The sum is 52x51x50x49x48.x4x3x2x1 and the answer is: 856,403,766,975,289,505,440, 883,277,824,000,000,000,000, that's roughly the same as an 8 with 67 zeros after.
Sign is called a factorial.
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With three cards A,B and C there are six different ways: ABC, ACB, BAC, BCA, CAB, CBA.
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