[Math] If five cards are drawn randomly from an ordinary deck, what is the probability of drawing exactly three face cards

Question

From an ordinary deck of $52$ cards, five are drawn randomly. What is the probability of drawing exactly three face cards? (assume no replacement)

I wrote the probability as a fraction with denominator $\binom{52}{5}$. For the numerator I wrote $\binom{12}{3}\binom{40}{2}$. My answer was approximately $.0660$.

Answer 1

I wrote the probability as a fraction with denominator $\binom {52} 5$. For the numerator I wrote $\binom {12}3\binom {40}{2}$. My answer was approximately $.0660$.

Yes.   $\left.\binom {12}3\binom{40}{2}\middle/\binom{52}{5}\right.$ is the probability for selecting three from the twelve face cards and two from the forty non-face cards, when drawing any five from all fifty-two cards without replacement.   That is the probability for the event you sought, as there are indeed those counts for face and non-face cards among a standard deck.