2 10 points When drawing 5cards from a wellshuffled standard

2. [10 points] When drawing 5-cards from a well-shuffled, standard deck of cards, what is the probability of drawing 3 diamonds, with and without replacement?

Solution

With replacement :

C(13,1) * C(39,4) / C(52,5) +C(13,1) * C(39,4) / C(52,5) + C(13,1) * C(39,4) / C(52,5)

= (0.4114)*(0.4114)*(0.4114)*(0.4114)

= 0.0286

Without Replacement

C(13,1)*C(39,4) / C(52,5) + C(12,1)*C(39,4) / C(51,5) + C(11,1)*C(39,4) / C(50,5)

= 0.4114 + 0.4201 + 0.4270 = 0.8471