Exercise · ZW-MULTINOMIAL-COEFFICIENT-006 · ★★☆ Intermediate
Find the coefficient of \(x^2yz\) in \((x+y+z)^4\).
Choose one option.
Show answer
- C. 12
Explanation
It is \(\binom{4}{2,1,1}=\frac{4!}{2!\,1!\,1!}=12\).
Review the concept: Multinomial coefficient
Multinomial coefficient \(\binom{n}{k_1,\dots,k_m}\): the number of ways to split \(n\) distinct objects into \(m\) labeled groups of sizes \(k_1,\dots,k_m\), where \(k_1+\cdots+k_m=n\).
\[\binom{n}{k_1,\dots,k_m}=\frac{n!}{k_1!\,k_2!\cdots k_m!}\]
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