Probability - Gravner -18.a

Question

A full deck of $52$ cards contains $13$ hearts. Pick $8$ cards from the deck at random
(a) without replacement compute the probability that you get no hearts.

Answer 1

1) Probability without replacement = $\Large \frac{39 \times 38 \times 37 \times 36 \times 35 \times 34 \times 33 \times 32}{52 \times 51 \times 50 \times 49 \times 48 \times 47 \times 46 \times 45}$$ = 0.05620$

 

2) Probability with replacement = $\left (\frac{39}{52} \right )^8 = 0.10011$