Question

# A bag contains 8 red, 3 white and 9 blue balls. If three balls are drawn at random, determine the probability that  (i) all the three balls are blue balls  (ii) all the balls are of different colours.

Solution

## Out of 20 balls, three balls can be drawn in 20C3 ways.  ∴ Total number of elementary ways = 20C3  (i) Let E be the event that all the three balls are blue ∴n(E)=9C3 ∴P(E)=9C320C3 =9×8×720×19×18=795 (ii) Let E be the event that all the balls are of different colour ∴n(E)=8C1×3C1×9C1 ∴P(E)=8C1×3C1×9C120C3=8×3×920C3=1895

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