The coefficients of $x^{2}y^{2},\ {y\mathcal{z}t}^{2}$ and$\ xy\mathcal{z}t$ in the expansion of ${(x + y + \mathcal{z +}t)}^{4}$ are in the ratio

Question

Dr. Abubacker · Accepted Answer

(b)
Coefficient of $x^{2}y^{2}$ in ${(x + y + \mathcal{z +}t)}^{4} = \frac{4!}{2!2!} = 6$ and
coefficient of ${y\mathcal{z}t}^{2}$ in $\left( x + y + \mathcal{z +}t ight)^{4}$
$= \frac{4!}{1!1!1!2!} = 12$
Also, coefficients of$\ xy\mathcal{z}t$ in
$\left( x + y + \mathcal{z +}t ight)^{4} = \frac{4!}{1!1!1!1!} = 24$
$	herefore$ Required ratio is $6:12:24 = 1:2:4$

Q. The coefficients of $x^{2}y^{2},\ {y\mathcal{z}t}^{2}$ and$\ xy\mathcal{z}t$ in the expansion of ${(x + y + \mathcal{z +}t)}^{4}$ are in the ratio

Explanation

Reviewed by Dr. Abubacker

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