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Question
A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that all the three balls are white
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Solution
Given that: Number of red balls = 8
Number of white balls = 5
P(All the three balls are white) = `(""^5C_3)/(""^13C_3)`
= `((5!)/(3!2!))/((13!)/(3!101))`
= `(5!)/(3!21) xx (3!10!)/(13!)`
= `(5!)/(2!) xx (10!)/(13 xx 12 xx 11 xx 10!)`
= `(5 xx 4 xx 3 xx 2!)/(21) xx 1/(13 xx 12 xx 11)`
= `(5 xx 4 xx 3)/(13 xx 12 xx 11)`
= `5/143`
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