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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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My solution | Comment 1 of 13
Three cards of a particular suit suit give (13*12*11) combinations.

The other two cards from a different suit form 39*38 combinations.

When we intermix the two sets this can be done in  5!/(3!2!) = 10 ways.

There are (4) posible suits.

The total number of  possible combinations of 5 cards with exactly three of the same suit is therefore, (13*12*11)*(39*38)*(10)*(4),
which divided by the toal number of 5 card combinations (52*51*50*49*48) gives a probability of 32.6%.

Edited on March 3, 2005, 2:37 pm
  Posted by ajosin on 2005-03-03 14:37:04

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