document.write( "Question 1120908: If 5 cards are drawn at random from a deck of 52, what is the probability of pulling 3 cards of one denomination and 2 cards of a second denomination? \n" ); document.write( "

Algebra.Com's Answer #736663 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "(1) # of ways of choosing 2 of the 13 denominations: 13C2 = (13*12)/2 = 78

\n" ); document.write( "(2) # of ways of choosing 1 of those 2 denominations to be the one to have 3 of a kind: 2C1 = 2

\n" ); document.write( "(3) # of ways of choosing 3 of the 4 cards of the first denomination: 4C3 = 4

\n" ); document.write( "(4) # of ways of choosing 2 of the 4 cards of the second denomination: 4C2 = 6

\n" ); document.write( "(5) # of ways of choosing 3 cards of one denomination and 2 of another: 78*2*4*6 = 3744

\n" ); document.write( "Probability of choosing 3 cards of one denomination and 2 of another: 3744/(52C5) = 3744/2598960 = .00144 (to 5 decimal places) \n" ); document.write( "

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