Question
A box contains 2 whits balls , 3 black balls and 4 red ball . In how many ways can 3 balls be drawn from the box , if at least one black ball is to be included in he draw ?
Answer: Option C
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We may have ( 1 black and 2 non black ) or 2 black and 1 non black ) or ( 3 black )
`:.` Required number of ways = `(3_(C_ 1) xx 6 _ (C _ 2)) + (3_(C_ 2) xx 6 _ (C _ 1))+ (3_(C_ 3)) `
= `(3 xx (6 xx 5)/(2 xx 1)) + ((3 xx 2)/(2 xx 1) xx 6)` + 1
= (45 + 18 + 1) = 64.
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