If you have 2000 candies distributed uniformly over 5 colors, what is the probability of getting more than 300 blue candies?
I was thinking of doing complementary counting, so
$$ 1-\sum_{i=0}^{300} {2000\choose{i}}\left(\frac 15\right)^{i}\left(\frac45\right)^{2000-i}$$
Would this be correct?