We choose $10$ random cards from a normal deck of cards($52$ cards). What is the probability that we get: a. $0$ aces b. maximum $3$ aces c. at least $1$ ace and at least one face card
That's the problem. I thought that since we're choosing $10$ cards from a deck, the sample space should be $$ \binom{10}{52} = \frac{52}{10!(52-10)!} \qquad \text{ (1)} $$
Then about a. question I thought that basically if $4$ aces are picked we should write $\dfrac{4}{52}\cdot \dfrac{3}{51}\cdot \dfrac{2}{50}\cdot\dfrac{1}{49}$ and then dividing this with (1) and then getting the derived set of this, we get the result.. I really don't know if I'm getting anything right here, so I'm in need of your insight.