How to eliminate the repeated case from polynomial counting?
assume a die throw $3$ times, do not allow repeated number appear
$(x+x^2+x^3+x^4+x^5+x^6)^3 - y$
how to count the repeated case, that should be minused in above polynomial counting? what is $y$ in terms of polynomial of $x$?
Mark six maple code
subs(z=0, diff(expand((1+z*x)*(1+z*x^2)*(1+z*x^3)*(1+z*x^4)*(1+z*x^5)*(1+z*x^6)*(1+z*x^7)*(1+z*x^8)*(1+z*x^9)*(1+z*x^10) *(1+z*x^11)*(1+z*x^12)*(1+z*x^13)*(1+z*x^14)*(1+z*x^15)*(1+z*x^16)*(1+z*x^17)*(1+z*x^18)*(1+z*x^19)*(1+z*x^20) *(1+z*x^21)*(1+z*x^22)*(1+z*x^23)*(1+z*x^24)*(1+z*x^25)*(1+z*x^26)*(1+z*x^27)*(1+z*x^28)*(1+z*x^29)*(1+z*x^30) *(1+z*x^31)*(1+z*x^32)*(1+z*x^33)*(1+z*x^34)*(1+z*x^35)*(1+z*x^36)*(1+z*x^37)*(1+z*x^38)*(1+z*x^39)*(1+z*x^40) *(1+z*x^41)*(1+z*x^42)*(1+z*x^43)*(1+z*x^44)*(1+z*x^45)*(1+z*x^46)*(1+z*x^47)*(1+z*x^48)*(1+z*x^49)), z$6));