If coefficient of x 2 y 3 z 4 in ( x + y + z ) n is A, (where A 0 , n ) then coefficient of x 4 y 4 z is

Question

If coefficient of $x^{2} y^{3} z^{4}$ in ${(x + y + z)}^{n}$ is A, (where $A \neq 0, n \in ℕ$ ) then coefficient of $x^{4} y^{4} z$ is

Smart Achievers · Accepted Answer

(3)

Since $x^{2} y^{3} z^{4}$ is occurring in the expansion of ${(x + y + z)}^{n}$ , so $n$ should be 9 only.

$Now A = \frac{9!}{2! \times 3! \times 4!} = 1260$

$Coefficient of x^{4} y^{4} z = \frac{9!}{4! \times 4!} = 630 = \frac{A}{2}$

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