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  3. consider the expansion of xyzn determine the coefficient of 563x5y6z3...

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

āˆ‘š‘Ž+š‘+š‘=š‘›(š‘›š‘Ž,š‘,š‘)=3š‘›,āˆ‘a+b+c=n(na,b,c)=3n,

where (š‘›š‘Ž,š‘,š‘)(na,b,c) is your answer and is known as a trinomial coefficient.

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