Question

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

• A. $\frac{37}{44}$
• B. $\frac{31}{44}$
• C. $\frac{21}{44}$
• D. $\frac{41}{44}$

Answer 1

Answer: (D)

$\frac{41}{44}$

Answer 2

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
$=1-\frac{15}{220}=1-\frac{3}{44}=\frac{41}{44}$