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  4. A bag contains 3 red, 4 white and 5 blue balls. If two balls are drawn at random, then the probability that they are different colours is

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Q. A bag contains $3$ red, $4$ white and $5$ blue balls. If two balls are drawn at random, then the probability that they are different colours is

KEAMKEAM 2016Probability

Solution:

Total number of balls $=3+4+5=12$
Favourable number of cases
$=^{12} C_{2}-\left({ }^{3} C_{2}+{ }^{4} C_{2}+{ }^{5} C_{2}\right)$
$=66-(3+6+10)=66-19=47$
Total number of cases $={ }^{12} C _{2}=66$ Hence, the required probability
$=\frac{\text { Favourable cases }}{\text { Total number of cases }}=\frac{47}{66}$