A bag contains 5 blue and 4 black balls. Three balls are

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A bag contains 5 blue and 4 black balls. Three balls are drawn at random. What is the probability that 2 are blue and 1 is black ?

1. 1/3
2. 2/5
3. 1/6
4. None of these

Correct Option: C

Let S be the sample space and E be the event of drawing 3 balls out of which 2 are blue and 1 is back .

Then, n (S)= Number of ways of drawing 3 balls out of 9=⁹c₃
= (9 x 8 x 7) / (3 x 2 x 1)
= 84 and

n(E) = Number of ways of drawing 2 balls out of 5 and 1 ball out of 4 .
= ⁵C₂ ⁴C₁₁
= (5 x 4) / (2 x 1) + 4 = 14

∴ P(E) = n(E)/n(S) = 14/84 = 1/6