Question

The coefficient of $(a^3.b^6.c^8.d^9.e.f)$ in the expansion of ${(a+b+c-d-e-f)}^{31}$ is

• A. $123210$
• B. $23110$
• C. $3110$
• D. none of these

Answer 1

The correct option is D none of these

Consider
$a^3{b}^6{c}^8{d}^{9}ef$
The sum of the powers is $3+6+8+9+1+1$
$=28$
However there is no $1$ in $(a+b+c-d-e-f{)}^{31}$
Hence the sum of the powers in each and every term should be equal to $31$.
However $28\ne 31$
Hence the term $a^3{b}^6{c}^8{d}^{9}ef$ does not exists.