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 `52//55` b. `53//55` c. `54//55` d. none of these

Options

A. `52//55`
B. `53//55`
C. `54//55`
D. none of these

Answer

B

Explanation

The total number of cases is `11!//(2! xx 2!)`. The number of favorable cases is `[11!//(2! xx 2!)] - 9!` Therefore, the required probability is
`=1 - (9! xx 4)/(11!) = (53)/(55)`