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}