Question

2 red, 4 white and 5 blue balls, balls of same colour are identical are placed on a line at random.The probability that no two blue balls are consecutive is given by

• A. $\frac{1}{33}$
• B. $\frac{1}{22}$
• C. $\frac{1}{110}$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$\frac{1}{22}$

Put $5$ blue balls between red and white walls i.e there are $7$ places where these $5$ balls can be put - $|R|R|W|W|W|W|$
Probability = $\frac{{}^7{C}_5\ast 6!/(4!\ast 2!)}{11!/(5!\ast 4!\ast 2!)}$
$=1/22$