3
Question
A box contained 2 white balls , 3 black $ 4 red balls . In how many ways can three balls be drawn from the box if atleast one black ball is to be included in draw (the balls of the same colour are different).
A box contained 2 white balls , 3 black $ 4 red balls . In how many ways can three balls be drawn from the box if atleast one black ball is to be included in draw (the balls of the same colour are different).
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Solution
The correct option is D 64
Total white balls =2Total black balls =3Total red balls =4The possibilities to draw three balls with atleast one black ball =(1 black+2 non black)+(2 black+1 non black)+(3 black+0 non black)⇒3C1×6C2+3C2×6C1+3C3×6C0⇒3C1×6C2+3C2×6C1+3C3×6C0⇒45+18+1⇒45+18+1⇒64
Total white balls =2
Total black balls =3
Total red balls =4
The possibilities to draw three balls with atleast one black ball =(1 black+2 non black)+(2 black+1 non black)+(3 black+0 non black)
⇒3C1×6C2+3C2×6C1+3C3×6C0⇒3C1×6C2+3C2×6C1+3C3×6C0
⇒45+18+1⇒45+18+1
⇒64
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