Probability

Concept:Use multiplication rule for dependent events without replacement.Explanation:Total balls: 13 (8 red, 5 white).First draw: 3 white from 5 white → favorable ways = $\binom{5}{3}=10$. Total ways for first draw = $\binom{13}{3}=286$.Probability first draw all white = $\frac{10}{286}$.After removing 3 white, remaining: 10 balls (8 red, 2 white).Second draw: 3 red from 8 red → favorable ways = $\binom{8}{3}=56$. Total ways for second draw = $\binom{10}{3}=120$.Probability second draw all red given first all white = $\frac{56}{120}$.Required probability = $\frac{10}{286} \times \frac{56}{120} = \frac{560}{34320} = \frac{7}{429}$.Answer:$\frac{7}{429}$