Algebra
Multinomial Theorem
MMTS_Full_Test_17
Grade 12
Question:
If coefficient of $x^2y^3z^4$ in $(x+y+z)^n$ is $A$ (where $A\ne 0$, $n\in\mathbb{N}$), then coefficient of $x^4y^4z$ is
$2A$
$\dfrac{nA}{2}$
$\dfrac{A}{2}$
$nA$
Step-by-Step Solution
Key Concept: Multinomial coefficients: $A=\frac{n!}{2!3!4!}$, new coefficient$=\frac{n!}{4!4!1!}$
$n=9$. $A=\frac{9!}{2!3!4!}=\frac{9!}{2\cdot 6\cdot 24}$. New coeff$=\frac{9!}{4!4!1!}=\frac{A}{2}$.
Correct Answer: 3