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Q.
A bag contains $5$ red balls, $3$ black balls and $4$ white balls are drawn at random. The probability that they are not of same colour is
TS EAMCET 2017
Solution:
We have,
$5$ red balls, $3$ black balls, $4$ white balls
Total numbers of balls $=(5+3+4)=12$
Three balls are drawn $={ }^{12} C_{3}=220$
Three balls are drawn of same colour
$={ }^{5} C_{3}+{ }^{3} C_{3}+{ }^{4} C_{3}=10+1+4=15$
Probability of are not same colour
$=1$ - Probability of same colour
$=1-\frac{15}{220}=1-\frac{3}{44}=\frac{41}{44}$