In a deck of 52 cards there are 13 hearts. If 3 are drawn from the deck, without replacement, what is the probability that all 3 cards will be hearts?

number triples with no restriction = C(52,3) = 22100

number of triples from the hearts = C(13,3) = 286
prob(3hearts) = 286/22100 = 11/850

To find the probability of drawing 3 hearts from a deck of 52 cards without replacement, we need to determine the number of favorable outcomes (drawing 3 hearts) and the total number of possible outcomes.

First, let's determine the number of favorable outcomes. Since there are 13 hearts in the deck, when you draw the first card, the probability of it being a heart is 13/52 (or 1/4).

After drawing the first heart, there are only 51 cards remaining in the deck, with 12 hearts left. So, the probability of the second card being a heart is now 12/51.

Similarly, after drawing the first two hearts, there are 50 cards remaining in the deck, with 11 hearts left. Thus, the probability of the third card being a heart is 11/50.

To find the probability of all three cards being hearts, we need to multiply these probabilities together:

(13/52) * (12/51) * (11/50)

Calculating these values, we get:

(13/52) * (12/51) * (11/50) = 0.0808

So, the probability of drawing 3 hearts from a deck of 52 cards without replacement is approximately 0.0808 or 8.08%.