6
votes
3answers
264 views

How many solutions are possible to this equation?

Given $$A+2B+3C=N $$ where $N$ is a given positive integer. $A ,B,C\in\mathbb{N}$ vary from $0$ to $\infty$. How many solutions will be there to this equation?
10
votes
5answers
329 views

What is the coefficient of the $x^3$ term in the expansion of $(x^2+x-5)^7$ (See details)?

I fail to see a simple way to answer this. As such, this is my long winded approach: Using the multinomial theorem, $$(x_1 + x_2 + \cdots + x_m)^n = \sum_{k_1+k_2+\cdots+k_m=n} {n \choose k_1, ...