Question

Find the coefficient of $a^2{b}^{5}d$ in the expansion of $(a+b-c-d{)}^8$.

Answer 1

The binomial coefficient of $(a{)}^2\times (b{)}^5\times (-c{)}^0\times (-d{)}^1=(-a^2{b}^{5}d)$ is given by $\frac{8!}{2!\times 5!\times 0!\times 1!}=168$

So, the numerical coefficient of $a^2{b}^{5}d=-1\times 168=-168$