SOLUTION: hi i need help on this question: five cards are drawn from an ordinary deck of 52 playing cards. what is the probability that the hand drawn is a full house (two of one kind, thre

Question 28525: hi
i need help on this question: five cards are drawn from an ordinary deck of 52 playing cards. what is the probability that the hand drawn is a full house (two of one kind, three of another kind)? I don't even know how to start this problem. Please help!
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
i need help on this question: five cards are drawn from an ordinary deck of 52 playing cards. what is the probability that the hand drawn is a full house (two of one kind, three of another kind)? I don't even know how to start this problem. Please help!
LET US BE FIRST CLEAR OF WHAT WE MEAN BY ONE KIND....
I TAKE IT AS SAME SUIT..THAT IS TWO SPADES AND THREE DIAMONDS SAY..OR LIKE THAT...ON THIS BASIS
TOTAL NUMBER OF COMBINATIONS TO DRAW 5 CARDS OUT OF 52 IS 52C5............I
THERE CARE 4 SUITS.WE WANT CARDS OF ANY 2 SUITS ONLY..SO LET US FIRST SELECT 2 SUITS FROM THE 4 AVAILBLE.
THIS CAN BE DONE IN 4C2 WAYS=6 WAYS.................II
NOW ONE COULD BE 2 CARDER AND ANOTHER COULD BE 3 CARDE
SO THE NUMBER OF POSSIBILITIES ARE =2 FROM THE ABOVE 2 SELECTED SUITS......III
THERE ARE 13 CARDS OF EACH SUIT.
NUMBER OF WAYS OF GETTING 2 CARDS OF SAME SUIT IS 13C2.....IV
NUMBER OF WAYS OF GETTING 3 CARDS OF SAME SUIT IS 13C3.....V
SO TOTAL NUMBER OF COMBINATIONS TO GET FULL HOUSE ARE II*III*IV*V
SUCCESSFULL COMBINATIONS =6*2*13C2*13C3
PROBABILITY=6*2*13C2*13C3/52C5

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