Question: consider the expansion of xyzn determine the coefficient of 563x5y6z3...
Consider the expansion of (𝑥+𝑦+𝑧)𝑛(x+y+z)n. Determine the
coefficient of 𝑥5𝑦6𝑧3x5y6z3 for 𝑛=14n=14.
In the general setting, we obtain that
where (𝑛𝑎,𝑏,𝑐)(na,b,c) is your answer and is known as a trinomial coefficient.