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A bag contains 5 red balls, 3 black balls and 4 white balls. Three balls are drawn at random. The probability that they are not of same colour is
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Verified Answer
The correct answer is:
$\frac{41}{44}$
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
$$
\begin{aligned}
& =1-\text { Probability of same colour } \\
& =1-\frac{15}{220}=1-\frac{3}{44}=\frac{41}{44}
\end{aligned}
$$
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
$$
\begin{aligned}
& =1-\text { Probability of same colour } \\
& =1-\frac{15}{220}=1-\frac{3}{44}=\frac{41}{44}
\end{aligned}
$$
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