from a pack of 52 playing cards, half of the cards are randomly removed without looking at them. From the remaining cards, 3 cards are drawn randomly. The probability that all are king is

hree cards can be drawn in 52C3 ways...= 22100 now we want at least two kings. there are 4 king in a pack of 52 cards. at least two means we can have 2 or 3 (4 kings we cant draw as maximum no of cards drawn is three only). drawing two kings = 4C2= 6 ways drawing three kings 4C3 = 4 ways but we have drawn three cards all together one card can be any card so when we draw 2 kings from 4 kings we have remaining 48 cards from which one card can be drawn so total ways = 4C2(drawing two kings) * 48C1 (drawing one card from the remaining cards) = 6* 48= 288 ways here we have multiplied the combinations bec in prob if our purpose is not solved then we have to multiply ..here we have to draw three cards..2 kings and one any of the cards ...so we have multiplied now when we draw three kings out of four kings then we dont have to draw any more cards from the remaining cards as in ques we have to draw three cards only so 4C3 * 48C0= 4 ways so total favourable ways= 288 + 4 = 292 ways so required probability is 292/22100 = .013

Total there are 4 kings..3 are to be drawn ..  = ⁴C₃
Total ways of drawing 3 cards = ⁵²C₃
P=⁴C_3/⁵²C_{3= 1/( 25*17"13)}