An urn contains 9 balls, 2 of which are white, 3 blue and 4 black. 3 balls are drawn at random from the urn. The chance that 2 balls will be of the same colour and the third of a different colour is

Step-by-step solution

Let E₁, E₂ and E₃ be the the events such that drawn ball is white, blue and black respectively. The required probability aligned &= ³ P₁ P (E₁ ) P (E₁ ) P( E )₁+ ³ P₁ P (E₂ ) P (E₂ ) P ( E ₂ ) &+ ³ P₁ P (E₃ ) P (E₃ ) P ( E ₃ ) &=3 2 9 1 8 7 7 +3 3 9 2 8 6 7 +3 4 9 3 8 5 7 &=3 [ 14+36+60 9 8 7 ]= 3 110 9 8 7 = 55 84 aligned