# How to find the total number of distinct terms in a certain expansion?

We know that $(1+x)^2$ has $3$ distinct terms because $(1+x)^n$ has $n+1$ terms going by the popular expansion starting from ${}_nC_0$ to ${}_nC_n$.

How do we find total number of distinct terms in expressions like $(a+b+c+f)^{40}$ and what's the generalized result?

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You might find this helpful Number of Terms in a Polynomial Expansion. Regards –  Amzoti Jan 21 at 17:46
SO the answer is $39C3$? –  Bazinga Jan 21 at 17:55