Question

A box contains $5$ green, $4$ yellow and $3$ white marbles. three marbles are drawn at random. What is the probability that all they are not of the same colour?

• A. $\frac{3}{44}$
• B. $\frac{3}{55}$
• C. $\frac{52}{55}$
• D. $\frac{41}{44}$

Answer 1

The correct option is D $\frac{41}{44}$

${\text{Total cases =}}^{12}{C}_3$

$=\frac{12\ast 11\ast 10}{3\ast 2\ast 1}=220$

$\text{Total cases of drawing same colour =}$

${}^5{C}_3$ ${+}^4{C}_3$ + ${}^3{C}_3=$

$\text{Probability of same color = \frac{15}{220}\\$

$=\frac{3}{44}$

Probability of not same color

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