What is the probability of drawing 12 marked cards?

Question

I have a deck of 40 cards. 16 of the cards are marked and the rest are unmarked. The deck is sufficiently shuffled. If I draw 12 cards off the top, what is the probability that each one would be marked?

Answer 1

The first card drawn has a $\frac {16}{40}$ chance to be marked.

Then, you have $39$ cards, $15$ of which are marked.

The second card drawn has a $\frac{15}{39}$ chance to be marked.

The third card drawn has a $\frac{14}{38}$ chance to be marked and so on.

Therefore the probability of drawing $12$ marked cards in a row is

$$\frac{16\times15\times14\times...\times5}{40\times39\times38\times...\times29}$$

Answer 2

Hypergeometric distribution gives here:$$\frac{\binom{16}{12}\binom{24}{0}}{\binom{40}{12}}$$