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Question

The letters of the word "RANDOM" are arranged in all possible ways. The number of arrangements in which there are 2 letters between 'R' and 'D' is

A
36
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B
48
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C
72
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D
144
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Solution

The correct option is D 144
Since there are 6 letters and there should be 2 letters between R and D.
R and D can be at
(1) 1,4 position
(2) 2,5 position
(3) 3,6 position
Now the remaing letters can be arranged in 4! ways, also R and D can be interchanged bwtween themselves in 2! ways.
Number of required arrangements will be =2!×4!+2!×4!+2!×4!=3×2!×4!=144

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