JEE Main · 2010 · 11 Apr 2010 · Offline · Probability

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An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is

(A) $\frac{2}{7}$ ✓ Correct
(B) $\frac{1}{21}$
(C) $\frac{2}{23}$
(D) $\frac{1}{3}$

Answer: (A)

Solution

There are

(3 9) = 84

equally likely ways to draw three balls. To get one of each colour we pick one red from three, one blue from four and one green from two, giving

3 \times 4 \times 2 = 24

favourable ways. The probability is

\frac{24}{84} = \frac{2}{7}

JEE Main · 2010 · 11 Apr 2010 · Offline · Single correct option

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