Question

The coefficient of $a^5{b}^7{c}^8$ in the expansion ${(ab+bc+ca)}^{10}$ is

• A. $2320$
• B. $2420$
• C. $2520$
• D. $2620$

Answer 1

The correct option is C $2520$

Considering
$\left(ab{)}^x\right(bc{)}^y(ac{)}^z$
Now $x+y+z=10$ ...(i)
Comparing with $a^5{b}^7{c}^8$ , we get
$x+y=7$ ...(ii)
$x+z=5$
$y+z=8$ ...(iii)
Solving i, ii and iii, we get
$z=3,x=2,y=5$
Hence the coefficient of $a^5{b}^7{c}^8$ will be
$\frac{10!}{3!2!5!}=2520$