A bag contains 20 black balls, 15 white balls and x orange balls. If one ball is drawn at random from the box and the probability of that ball being white is 3/8. If 3 balls are drawn randomly, then find the probability that there are no white balls.
A. 78/321
B. 115/494
C. 48/121
D. 55/216
E. None of these
Sol:
Number of orange balls=x
15C1/(35+x)=3/8
15*8=(35+x)*3
120=105+3x
15/3=x
x=5
Required probability=25C3/40C3
=(25*24*23)/(40*39*38)
=115/494
