The number of arrangements of the letters of the word ARRANGEMENT in which two Es' do not occur adjacently is
The number of arrangements of the letters of the word ARRANGEMENT in which two Es' do not occur adjacently is
$\frac{9}{8}(10) !$
$\frac{9}{4}(10) !$
$\frac{9}{16}(10) !$
$\frac{9}{32}(10)!$
Solution
Total arrangements $=\frac{\lfloor 11}{\lfloor 2 \cdot 2 \cdot|2 \cdot| 2}$
Number of arrangement in which two E occur together $=\frac{10}{2 \cdot 2 \cdot 2 \cdot 2}$ $=\frac{10.9}{16}=\frac{9}{16}\lfloor 10$