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Probability test (Posted on 2005-03-03) Difficulty: 2 of 5
Five cards are drawn from a pack of 52 cards. What is the probability that exactly three of them are of the same suit.

See The Solution Submitted by Sandeep    
Rating: 3.0000 (3 votes)

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re: My solution (a crosscheck) | Comment 5 of 13 |
(In reply to My solution by ajosin)

We can check the solution without doing a simulation,

a) Combinations with 3 of the same suit are 13*12*11*39*38*10*4

b) Combinations with 4 of the same suit are 13*12*11*10*39*5*4

c) Combinations with 5 of the same suit are 13*12*11*10*9*1*4

d) Combinations 2 of one suit, 2 of another, and 1 of another are, 13*12*13*12*26*30*6 (we need a 6 instead of a 4 at the end because the two double suits can be selected in 6 different ways)

e) Combinations whith two cards of one suit and one of each other suit are, 13*12*13*13*13*60*4

Any 5 cards fall in one and only one of the categories in a)-e), therefore a)-e) represent all possible 5 card combinations and should add up  52*51*50*49*48. They do indeed. Here is their probabilty distribution,

a) 32.6%
b) 4.3%
c) 0.2%
d) 36.5%
e) 26.4%

  Posted by ajosin on 2005-03-03 15:30:44

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