I just read in Cengage's Algebra that in order to find the number of some constraint bounded solutions of an equation (say, non negative integral), it would be the same as the coefficient of $x^n$ in expansion of $(x^1 + x^2 + ... x^\text{(max value attainable by variable)})^\text{(no. of variables)}$. How come ? What is the logic behind the coefficient of $x^n$ and no. of solutions being same ?
2026-03-25 23:35:54.1774481754
Application of Multinomial Theorem
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