$\begin{array}{1 1}(A)\;\large\frac{1}{62}\\(B)\;\large\frac{1}{72}\\(C)\;\large\frac{1}{52}\\(D)\;\text{None of these}\end{array} $

- Required probability =$\large\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Step 1:

Given word ALGORITHM

Number of letters in the word =9

The word is arranged randomly.

$\therefore$ Total number of outcomes n(S)=9!

Given GOR have to remain together

Thereby considering GOR as a single letter

$\therefore$ No of letter=7

Number of favorable outcomes n(E) =7!

Step 2:

$\therefore$ Required probability =$\large\frac{n(E)}{n(S)}$

$\Rightarrow \large\frac{7!}{9!}$

$\Rightarrow \large\frac{1}{9\times 8}$

$\Rightarrow \large\frac{1}{72}$

Hence (B) is the correct answer.

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