Question

A bag contains $6$ red, $4$ white and $8$ blue balls. If three balls are drawn at random, then find the probability that all the three balls are red.

• A. $\frac{7}{102}$
• B. $\frac{5}{204}$
• C. $\frac{3}{204}$
• D. $\frac{2}{204}$

Answer 1

The correct option is B $\frac{5}{204}$

no of Red balls $=6$

no of White balls $=4$

no of Blue balls $=8$

no of way to select three red balls $={}^6{C}_3$

no of way to select three balls $={}^{18}{C}_3$

P(selected balls are red) $=\frac{{}^6{C}_3}{{}^{18}{C}_3}=\frac{6\times 5\times 4}{18\times 17\times 16}$

$=\frac{5}{204}$