# Question: consider the expansion of xyzn determine the coefficient of 563x5y6z3...

###### Question details

Consider the expansion of (š„+š¦+š§)š(x+y+z)n. Determine the
coefficient of š„5š¦6š§3x5y6z3 for š=14n=14.

Your answer:Ā Ā

In the general setting, we obtain that

āš+š+š=š(šš,š,š)=3š,āa+b+c=n(na,b,c)=3n,

where (šš,š,š)(na,b,c) is your answer and is known as a trinomial coefficient.