Question

Assume that there are 16 frozen dinners: 8 pasta, 4 chicken, and 4 seafood dinners. The student selects 5 of them.

What is the probability that at least 2 of the dinners selected are pasta dinners?

I tried this:
(c(8,2)c(8,3)+c(8,3)c(8,2)+c(8,4)c(8,1))/c(16,5) = 3696/4368

But this is incorrect. I have no idea what other way to solve this. Any sugguestions?

Answer 1

You forgot to include c(8,5)c(8,0) in the summation. You can also compute the complementary probability of 1 or less first. Then you only need to sum over two terms.