Question

The coefficient of $x^3{y}^4{z}^5$ in the expansion of $(xy+yz+zx{)}^6$, is

• A. $120$
• B. $20$
• C. $30$
• D. $60$

Answer 1

The correct option is D $60$

${(xy+yz+zx)}^6=....+\frac{6!}{a!b!c!}{\left(xy\right)}^a{\left(yz\right)}^b{\left(zx\right)}^c$

$\Rightarrow x^{a+c}{y}^{a+b}{z}^{b+c}$

$a+c=3,b+c=5,a+b=4$

$\therefore b-a=2,b+a=4$

$b=3,a=1,c=2$

Coefficient of $x^3{y}^4{z}^5=\frac{6!}{3!1!2!}=60$