Combinations of percentages. How would I calculate all possible combinations of given percentages so that none of the combinations is less than 51%? For example one such combination of


*

*24%

*23%

*21%

*17%

*8%

*7%


would be 23% + 24% + 7% = 54%.
 A: Following this we can find what you want from the generating function of partitions without repetition based on $k$ numbers for $k\in \{7,8,17,21,23,24\}$. Then
$$
\begin{align*}
SQ:=&(1+x^7)(1+x^8)(1+x^{17})(1+x^{21})(1+x^{23})(1+x^{24})\\
=&\,x^{100}+x^{93}+x^{92}+x^{85}+x^{83}+x^{79}+x^{77}\\
&+2x^{76}+x^{75}+x^{72}+x^{71}+x^{70}+2x^{69}+2x^{68}\\
&+x^{64}+2x^{62}+x^{61}+x^{60}+x^{59}+x^{56}+2x^{55}\\
&+x^{54}+2x^{53}+2x^{52}+x^{51}+x^{49}+2x^{48}+2x^{47}\\
&+x^{46}+2x^{45}+x^{44}+x^{41}+x^{40}+x^{39}+2x^{38}\\
&+x^{36}+2x^{32}+2x^{31}+x^{30}+x^{29}+x^{28}+x^{25}\\
&+2x^{24}+x^{23}+x^{21}+x^{17}+x^{15}+x^8+x^7+1
\end{align*}
$$
Now, from the previous expression, we must count the coefficients of the exponents that are equal or bigger to $51$, that is if we set
$$f(x):=x^{100}+x^{93}+x^{92}+x^{85}+x
   ^{83}+x^{79}+x^{77}+2
   x^{76}+x^{75}+x^{72}+x^{71}
   +x^{70}+2 x^{69}+2
   x^{68}+x^{64}+2
   x^{62}+x^{61}+x^{60}+x^{59}
   +x^{56}+2 x^{55}+x^{54}+2
   x^{53}+2
   x^{52}+x^{51}$$
then $f(1)$ is what you want.
