问题
I am a mathematics student and was given a proof detailed in this link.
Out of curiosity I tried setting that up in a an Excel table with columns as N and rows as K, so that:
=COMBIN(R$6,$B16)-COMBIN(R$6-1,$B16)-COMBIN(R$6-1,$B16-1)
should equal 0. For the most part it does but sometimes I get odd results. For example:
=COMBIN(110,35)-COMBIN(110-1,35)-COMBIN(110-1,35-1)=0
and
=COMBIN(110,45)-COMBIN(110-1,45)-COMBIN(110-1,45-1)=0
but
=COMBIN(110,40)-COMBIN(110-1,40)-COMBIN(110-1,40-1)=633318697598976
Can somebody tell me why this is happening?
回答1:
I’m afraid the answer has to be the lack of precision in Excel (15 digits max) but maybe that is not really a good enough answer.
Excel’s =COMBIN() function for A2 (say 110) and B2 (say 35) can be broken down as:
=FACT(A2)/(FACT(A2-B2)*FACT(B2))
The top part of the image below shows this (and confirms your results!):
The bottom part breaks that formula down into its components, showing that the largest element has a value 1.5882E+178. That is well within Excel’s limit for formulae of +/-1.7976931348623158e+308 but presumably is actually something between:
15882455415227300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
and
15882455415227500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
which I guess is the problem.
What puzzles me is that sticking with 110, the discrepancies arise only 29 times in the B2 range 1-109 – but for any explanation of that it may be best to revert to Mathematics!
来源：https://stackoverflow.com/questions/18746815/odd-results-using-the-combin-function