Question

Word from the letters of the word $PROBABILITY$ are formed by taking all letters at a time.The probability that both $B^{\prime }s$ are not together and both $I^{\prime }s$ are not together is

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

Answer 1

Answer: (B)

$53/55$

$PROBABILITY$

Let us treat $2B^{\prime }s$ and $2I^{\prime }s$ together.

$\therefore$ Total letters know $7+2=9$

$\Rightarrow$ no. of ways $=9!\times 2$

Total ways $=\frac{11!}{2!2!}$

So probability $=1-\frac{2\times 9!}{11!}\times 2!\times 2!$

$=\frac{53}{55}.$

Hence, the answer is $\frac{53}{55}.$