An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is
Balls in urn = 9
3 balls can be drawn in 9C3 ways.
To draw the balls of same colour, we can select balls all three red, all blue or all black.
P(ball of same colour) = P(all blue) or P(all black) or P(all red)
P(all red) = not possible as we have to select 3 balls but there are only 2 red balls.
∴ P(All red) = 0
P(all black) =
And P(all blue) =
∴ P(ball of same colour) = P(all blue) or P(all black) or P(all red)
⇒ P(ball of same colour) = P(all blue) + P(all black) + P(all red)
= 1/84 + 1/21 + 0 = 5/84
Our answer matches with option (a)
∴ Option (a) is the only correct choice