Question

If the letters of the word 'PROBABILITY' are written down at random in a row, then probability that two B's are together, is

• A. $\frac{2}{11}$
• B. $\frac{10}{11}$
• C. $\frac{3}{11}$
• D. $\frac{6}{11}$

Answer 1

The correct option is A $\frac{2}{11}$

Total number of ways in which the letters of the word 'PROBABILITY' can be arranged in a row$=\frac{11!}{2!2!}$
Number of ways in which two B's are together $=\frac{10!}{2!}$
$\therefore$ Required probability $=\frac{\frac{10!}{2!}}{\frac{11!}{2!2!}}=\frac{10!\times 2!}{11!}=\frac{2}{11}$