Question

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

• A. $\frac{40}{44}$
• B. $\frac{44}{41}$
• C. $\frac{41}{44}$
• D. $\frac{40}{39}$
• E. $\frac{44}{39}$

Answer 1

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

$n\left(E\right)={}^5{C}_3{+}^4{C}_3{+}^3{C}_3=10+4+1=15n\left(S\right)={}^{12}{C}_3=220P=n\left(E\right)/n\left(S\right)=\frac{15}{220}=\frac{3}{44}$
Required probability $=\frac{1-3}{44}=\frac{41}{44}$