A standard deck of cards contains 52 cards The cards can be

A standard deck of cards contains 52 cards The cards can be classified by one of The 4 suits (hearts, diamond, clubs, or spades) The cards can also be classified by their rank (Ace. 2. 3. 4. 5.6. 7. 8. 9. 10. Jack. Queen, or King) Each suit contains one of each rank A 5-card hand would be a collection of 5 distinct cards from The deck For The purposes of this homework it will not be helpful thinking of The 5card hand as being ordered Suppose you we randomly given a 5-card hand. What\'s The probability that your hand has 3 matching cards of a rank and 2 matching cards of another rank? To be clear. we are talking about hands like, for example. 3 of hearts. 3 of (diamonds. 3 of clubs Jack of spades. and Jack of clubs.

Solution

There are 52C5 = 2598960 ways to choose 5 cards.

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There are 13 suits to choose 4C3 = 4 cards for a triple.

Then, there are 12 remaining suits to choose 4C2 = 6 pairs each.

Thus, there are 13*4*12*6 = 3744 ways to do the task.

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Thus,

Probability = 3744/2598960 = 0.001440576 = 0.0014 [ANSWER]