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MHT CET · Maths · Probability

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 colours, is

  1. A \(\frac{1}{3}\)
  2. B \(\frac{2}{7}\)
  3. C \(\frac{1}{21}\)
  4. D \(\frac{2}{23}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{2}{7}\)

Step-by-step Solution

Detailed explanation

\(\text {Required probability } =\frac{{ }^3 \mathrm{C}_1 \times{ }^4 \mathrm{C}_1 \times{ }^2 \mathrm{C}_1}{{ }^9 \mathrm{C}_3}\)
\(=\frac{3 \times 4 \times 2}{\left(\frac{9!}{3!6!}\right)}=\frac{24 \times 6}{9 \times 8 \times 7}=\frac{2}{7}\)