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If nc2+nc3+nc4+...+ncn=31-n How much n??

That's n=5. Why?

Why !!!????i think it is in Binomial Theorem but i don't know how!

You mean you want to know how to find n?

31 - n = nc2 + ... + ncn = (nc0 + ... + ncn) - nc0 - nc1 = 2^{n} - nc0 - nc1 = 2^{n} - 1 - n

Add n+1 on both sides and you have

32 = 2^{n} -> n = log_{2} 32 = 5

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