Question

Words from the letters of the word $PROBABILITY$ are formed by taking all at a time. The probability that both $B^{\prime }s$ are together and both $I^{\prime }s$ are together is

• A. $1/55$
• B. $2/55$
• C. $4/165$
• D. $3/55$

Answer 1

The correct option is B $2/55$

Probability is a word that has $1P,1R,1O,2B,1A,2I,1L,1T,1Y$.....Total ways it can be arranged = $(11!/2!\times 2!)$

Now for finding ways when both $I‘s$ and both $B‘s$ are together...$9!$

Probability = $4/(11\ast 10)=4/110=2/55$