If the letters of the word 'PROBABILITY' are written down at random in a row, then probability that two B's…
If the letters of the word 'PROBABILITY' are written down at random in a row, then probability that two B's are together, is
$\frac{2}{11}$
$\frac{10}{11}$
$\frac{3}{11}$
$\frac{5}{11}$
Solution
Total number of ways in which the letters of the word 'PROBABILITY can be amanged in a row $=\frac{11!}{2!2 !}$
Number of ways in which two B's are togother $=\frac{10!}{2!}$
$\therefore$ Required probability
$=\frac{\frac{10}{2 !}}{\frac{11!}{2!2!}}=\frac{10 ! \times 2!}{11!}=\frac{2}{11}$