Q56 / 160 · AP EAMCET 2023 (16 May Shift 2) · Mathematics

The number of arrangements of the letters of the word ARRANGEMENT in which two Es' do not occur adjacently is

  • A
    $\frac{9}{8}(10) !$
  • B
    $\frac{9}{4}(10) !$
  • Correct answer
    C
    $\frac{9}{16}(10) !$
  • D
    $\frac{9}{32}(10)!$

Solution

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

Hence, the correct answer is option: 'C'.

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