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A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that:
(i) All the three balls are white
(ii) All the three balls are red

According to the question, a bag contains 8 red and 5 white balls.

By using the formula of probability, we get,

P (E) = favourable outcomes / total possible outcomes

Total number of ways of drawing three balls at random is ${ }^{13} \mathrm{C}_{3}$

n (S) = 286

(i) Let E be the event of getting all white balls

E= {(W) (W) (W)}

$n(E)={}^5C_3=10$

P (E) = n (E) / n (S)

= 10 / 286

= 5/143

(ii) Let E be the event of getting all red balls

E = {(R) (R) (R)}

$n(E)={}^8C_3=56$

P (E) = n (E) / n (S)

= 56 / 286

= 28/143