Three cards are drawn without replacement from a wellshuffle

Three cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the third card drawn is a heart?

Solution

case 1 : no heart in first two draws then probability of heart in 3rd draw= (4/(52-1-1)) =4/50 =0.08

case 2 : heart in first draw then probability of heart in 3rd draw=3/(52-1-1)) =(3/50)=0.06

case 3 : heart in 2nd draw then probability of heart in 3rd draw=3/(52-1-1)) =(3/50)=0.06

case 4 : heart in first,second draw draw then probability of heart in 3rd draw= (2/50)=0.04

now total probability that 3rd card drawn is heart is =0.08+0.06+0.06+0.04=0.24

final probability = sum of all probabilities