**Question **: Words from the letters of the word PROBABILITY are formed by taking all letters at a time. The probability that both B’s are not together and both i’s are not together is

(A) 52/55

(B) 53/55

(C) 54/55

(D) none of these

**Answer **: option (B)

**Solution **:

The total number of cases is 11!/2! × 2!. the number of favorable cases is [11! (2! × 2!)] -9!.

Therefore the required probability is

1-\dfrac{9!\times 4}{11!}=\dfrac{53}{55}