Q50 / 160 · TS EAMCET 2017 · Mathematics
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
- A$\frac{37}{44}$
- B$\frac{31}{44}$
- C$\frac{21}{44}$
- Correct answerD$\frac{41}{44}$
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
$$
\begin{aligned}
& =1-\text { Probability of same colour } \\
& =1-\frac{15}{220}=1-\frac{3}{44}=\frac{41}{44}
\end{aligned}
$$
Hence, the correct answer is option: 'D'.