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

Algebra ->  Probability-and-statistics -> 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      Log On


   

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) About Me  (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 %28%2813C2%29%284C2%29%284C2%29%29%2F%2852C4%29

or 216%2F20825 or as an approximate decimal 0.01037214886

Edwin