Interesting

To get the sum of coefficients in the expansion of $(a+b+c)^{n}$ , we can substitute $a=1$ , $b=1$ , and $c=1$ to $(a+b+c)^{n}$

It is equal to $(1+1+1)^{n}=3^{n}$

Then, the sum of coefficients in the expansion of $(a+b+c)^{17}$ is $3^{17}=129140 \color{#3D99F6}{163}$

$S=1+6+3=\boxed{10}$

The sum of the coefficients in expansion of

${ (a+b+c) }^{ n }$ = ${ 3 }^{ n }$ . The rest is clear.

 3^17= 129140163. Thus answer is 10.