Question

Different words are being formed by arranging the letters of the word ARRANGE. All the words obtained are arranged in the form of a dictionary

The number of words in which no two A's are together

• A. 1260
• B. 900
• C. 360
• D. None of these

Answer 1

The correct option is B 900

Total number of words $=$ Number of words in which particular things are always together + never together

$\therefore$ Number of words in which no two A's are together $=$ Total words -Number of words in which A's are together

$=\frac{7!}{2!2!}-\frac{6!}{2!}$ $=1260-360=900$

$\therefore$ option $\left(B\right)$ is correct.