# SOLUTION: A standard deck of 52 playing cards consists of four different suits and 13 cards of different ranks in each suit. Four cards will be drawn at random without replacement from thi

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 Click here to see ALL problems on Mixture Word Problems Question 246889: A standard deck of 52 playing cards consists of four different suits and 13 cards of different ranks in each suit. Four cards will be drawn at random without replacement from this deck. The probability that the four cards will be all the same suit is k times the probability that they will be all the same rank. What is the value of k?Answer by josmiceli(9661)   (Show Source): You can put this solution on YOUR website!If I want P1(4 cards same suit), I don't care what the 1st card is, so I'll call P1(1st card) = , which means I'm certain to get any one of the cards. Now I have that card, and it is a certain suit, say clubs. There are 12 clubs left, so my chances of getting another club is Now there are 11 clubs left , and ----------------------------------- There are 13 groups of 4 cards which are the same rank I don't care what the 1st card is I've got the 1st card. Say it is a 9 is P2(another 9) is P3(another 9) is P4(another 9) -------------------------------------- given: Multiply right side by