Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all the four cards are king?

Explanation

Let `E_(1),E_(2),E_(3) and E_(4)` are the events that the first, seond, third and fourth card is king, respectively.
`therefore P(E_(1)capE_(2)capE_(3)capE_(4))=P(E_(1))cdotP(E_(2)//E_(1))cdotP(E_(3)//E_(1)capE_(2))cdotP[E_(4)//(E_(1)capE_(2)capE_(3)capE_(4))]`
`=4/52cdot3/51cdot2/50cdot1/49=24/(52cdot51cdot50cdot49)`
`=1/(13cdot17cdot25cdot49)=1/270725`