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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 one ball is red and two balls are white
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Solution
Given that: Number of red balls = 8
Number of white balls = 5
P(one ball is red and two balls are white) = `(""^8C_1 xx ""^5C_2)/(""^13C_3)`
= `(8 xx 10)/((13!)/(3! xx 10!))`
= `(8 xx 10)/(13!) xx (3! xx 10!)/1`
= `(8 xx 10 xx 3 xx 2 xx 10!)/(13 xx 12 xx 11 xx 10!)`
= `(8 xx 10 xx 6)/(13 xx 12 xx 11)`
= `40/143`
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