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 Feb16 accepted $4$ judges must distribute grades from $1$ to $6$ for each participant. In how many ways one can score $22$ points? Feb16 comment $4$ judges must distribute grades from $1$ to $6$ for each participant. In how many ways one can score $22$ points? Yes. Josh B. gave a clue in the comments. I forgot to calculate for $23,24$ points too. Feb16 comment $4$ judges must distribute grades from $1$ to $6$ for each participant. In how many ways one can score $22$ points? @JoshB. Oh, that is it then. I guess I forgot to count the rest of the points. $23,24$ points also result in a finalist. Feb16 asked $4$ judges must distribute grades from $1$ to $6$ for each participant. In how many ways one can score $22$ points? Feb16 asked Is it possible to represent any sequence as the coefficients of arbitrary generating functions? Feb16 asked What is the coefficient of $x^{10}$ in $\left[ \frac{1-x^3}{1-x}\right]\left[ \frac{1-x^4}{1-x}\right]\left[ \frac{1}{1-x}\right]^2$? Feb13 asked Doubts on the workings of generating functions? Feb13 comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice? Who downvoted this?! Feb12 reviewed Approve Second Partial Derivative Test for a Three-Variable Function Feb12 comment Why to ignore the factorials as part of the coefficients in the exponential generating function? Yes. You're assuming it's that way by definition. But for example, $0!=1$, people usually say that this is true because of definition, but it's actually defined that way because it yields desirable answers in a lot of concepts. The concept of factorial per se would break if $0!=0$ in $a\choose 0$, for example. Feb11 asked Why to ignore the factorials as part of the coefficients in the exponential generating function? Feb10 comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice? Thanks for your answer. Could you clarify a little bit on your steps? Your answer seems really interesting, but it's not really clear what you are doing there: It seems that you're using techniques of analysis (some kind of treatment of series I never seen before). [Please, do not erase your answer because of my stupidity, leave it there and write a little bit on every step. Some day this answer might enhance my knowledge a lot]. Feb9 accepted How to obtain the chromatic polynomial of $C_5$? Feb9 accepted What is the connection with $g=1+\frac{1}{g}$ and $G_n= 1+\frac{1}{G_{n-1}}$? Feb8 comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice? I don't understand how you go from $1$ to $2$ here. Feb8 comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice? Oh, nevermind. I remember it: $\frac{(x-x^7)^4}{(1-x)^4}=(x-x^7)^4\times \frac{1}{(1-x)^4}=(x-x^7)^4\times (1-x)^{-4}$. Feb8 comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice? One silly thing: How does $\left[\frac{x-x^7}{1-x}\right]^4$ becomes $x^4(1-x^6)^4(1-x)^{-4}$? Feb8 comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice? Why if the sum from $r=0$ make it become $\frac{x-x^7}{1-x}$? Feb8 comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice? Excuse me, isn't it: $\displaystyle \sum_{r=1}^6 x^r=\frac{1-x^7}{1-x}$ ? Feb8 comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice? Great! Thank you very much.