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
  1. $\frac{9}{8}(10) !$
  2. $\frac{9}{4}(10) !$
  3. $\frac{9}{16}(10) !$
  4. $\frac{9}{32}(10)!$

Solution

Total arrangements $=\frac{\lfloor 11}{\lfloor 2 \cdot 2 \cdot|2 \cdot| 2}$ Number of arrangement in which two E occur together $=\frac{10}{2 \cdot 2 \cdot 2 \cdot 2}$ $=\frac{10.9}{16}=\frac{9}{16}\lfloor 10$

Asked in: AP EAMCET 2023 (16 May Shift 2)

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