# SOLUTION: Find the number of different 5-card hands that can be dealt from a standard deck of 52 playing cards? Find the probability that 4 kings and a queen are randomly drawn from a sta

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 Click here to see ALL problems on Permutations Question 31564: Find the number of different 5-card hands that can be dealt from a standard deck of 52 playing cards? Find the probability that 4 kings and a queen are randomly drawn from a standard deck of 52 playing cards?Found 2 solutions by longjonsilver, venugopalramana:Answer by longjonsilver(2297)   (Show Source): You can put this solution on YOUR website!ok....52 cards: there are 52 possible choices...Pick one there are now 51... Pick second there are now 50... pick the third there are now 49... pick 4th there are now 48... pick 5th So, possible number of variations are: 52*51*50*49*48. However, some of these are repeated. How many are repeated? Well, look at an easier example: Pick 2 letters from ABCDE: AB BA CA DA EA AC BC CB DB EB AD BD CD DC EC AE BE CE DE ED So from 5 choices we have 5*4 --> 20. And yet AB is the same as BA, in terms of them being playing cards...the hand is the same irrespective of having A then B dealt or B then A...the hand is still "A and B". Looking, there are actually only 10 different "hands" in this example: 20/2!. Another example: pick 3 from the 5: ABC BCD CDE ABD BCE ABE BDE ACD ACE ADE Here there are 10 solutions gotten from (5*4*3)/3! So, for your question, we get 52*51*50*49*48/5! which is 2,598,960 different hands This gives us that the probability of a particular hand = 1/2598960 Now P(4 kings and a queen) is actually 4 potential hands... 4K and Q clubs or 4K and Q diamonds or 4K and Q hearts or 4K and Q spades so, P(4K and a Q) = 4*(1/2598960) 4/2598960 As you can see, the odds are very small of this happening jon. Answer by venugopalramana(3286)   (Show Source): You can put this solution on YOUR website!Find the number of different 5-card hands that can be dealt from a standard deck of 52 playing cards? =52C5=52!/(52-5)!5!=52*51*50*49*48/5*4*3*2*1=52*51*10*49*2 Find the probability that 4 kings and a queen are randomly drawn from a standard deck of 52 playing cards? 4 KINGS CAN BE GOT FROM 4 KINGS IN =4C4=1 WAY 1 QUEEN CAN BE GOT FROM 4 QUEENS IN 4C1=4 WAYS. SO NO.OF SUCCESSFULL COMBINATIONS =1*4=4 PROBABILITY OF SUCCESS =4/(52*51*10*49*2)=1/(52*51*5*49)