Question

If the letters of the word PROBABILITY are written down at random in a row, the 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 $\frac{2}{11}$

The total number of ways in which the letters of the word PROBABILITY are arranged is $\frac{11!}{2!2!}$

If two B's are together, it can be considered as one object.
So, total number of ways in which the letters of the word PROBABILITY are arranged such that two B's are together is $\frac{10!}{2!}$

The probability that two B-s are together is, $\frac{10!/2!}{11!/2!2!}=\frac{2}{11}$