SOLUTION: Given a standard deck of 52 playing cards, what is the probability of drawing four cards that form two different pairs. For example 2 queens and 2 tens, or 2 fives and 2 sevens. Th

Question 1101329: Given a standard deck of 52 playing cards, what is the probability of drawing four cards that form two different pairs. For example 2 queens and 2 tens, or 2 fives and 2 sevens. The pairs must be different from each other, four of the same kind does not qualify.
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

Choose the 2 ranks for the pair in 13C2 ways.
Choose the 2 suits for the lower ranked pair in 4C2 ways.
Choose the 2 suits for the lower ranked pair in 4C2 ways.

So the numerator of the probability is (13C2)(4C2)(4C2)

The denominator is (52C4)

So the probability is 

or  or as an approximate decimal 

Edwin

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