Combinatorics..#1

Using the multinominal theorem, the multinominal coefficients are $\frac{n!}{k_1!k_2!k_3!.....k_m}$ where n is the power to which the original expression was raised and $k_1+k_2+k_3.....k_m= n$ .

So we want to work out the coefficient of $abc^3de^2$ = $a^1b^1c^3d^1e^2$ . In this case n = 8 and $k_1, k_2, k_3...k_m$ = 1, 1, 3, 1, 2 (the powers in the expression $abc^3de^2$ ).

This means that the coefficient is $\frac{8!}{1! 1! 3! 1! 2!}$ = $\boxed{3360}$ .