contestada

Five cards are selected without replacement from a pack of 52 playing cards. What is the probability of exactly 3 hearts?

I can find an equation for exactly 3 hearts, but I can't turn the other two cards in terms of combinatorics or permutations for some reason.

I've tried:
[tex] \left(\begin{array}{cc}4\\1\end{array}\right) \left(\begin{array}{cc}13\\3\end{array}\right)[/tex] for the selection of exactly three hearts.

Thanks.

Respuesta :

LammettHash
There are 13 total hearts in the deck, which leaves 39 non-hearts. You're drawing a hand of five cards, so the probability of getting exactly 3 hearts is

[tex]\dfrac{\binom{13}3\binom{39}2}{\binom{52}5}=\dfrac{2717}{33320}[/tex]

as required.

Otras preguntas