Here's my question, which is similar to the one I asked a couple weeks ago:
Find the coefficient of $x^4$ in the expansion of $(1+x+x^2+x^3)^7$.
I was suggested to use the Binomial Theorem, but it would become very tedious and just decided to use the Multinomial Theorem instead. So I need to find the terms that have $x^4$ in them. 3 such instances do occur and they are:
$$1^5 \cdot (x)^1 \cdot (x^2)^0 \cdot (x^3)^1$$ $$1^5 \cdot (x)^0 \cdot (x^2)^2 \cdot (x^3)^0$$ $$1^3 \cdot (x)^4 \cdot (x^2)^0 \cdot (x^3)^0$$
Notice that all of the exponents add up to $7$. I'm supposed to get $203$ as my result (verified using Wolfram), but I got $98$ as my answer. I believe I'm missing some other factors, but cannot find any more other than those $3$.