- #1

Amad27

- 412

- 1

What is the probability of getting exactly 6 questions correct on this test?

The answer is: $$\binom{10}{6} (0.2)^6 (0.8)^4$$

I see that, there $\binom{10}{6}$ ways of selecting $6$ correct questions here.

But then, take a question like:At a soccer match there are 230 all-stars and 220 half-stars. You pick five people from the crowd. What is the probability that exactly two are all-stars?

I would say:

$$P = \frac{\binom{230}{2} \cdot \binom{220}{3}}{\binom{450}{5}}$$

My question is, arent there also many ways to choose the $2$ all stars out of the $230$? So wouldn't you multiply by $\binom{230}{2}$ again?