Question

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

Answer 1

Hey there !!

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R_ _ D_ _
_R_ _ D_
_ _ R_ _ D  

These are the different arrangements in which R and D have two letters between them. The remaining 4 places can be filled in ⁴P₄ ways.

So

Total possible arrangements =2*3*⁴P₄
4P4 is multiplied with 2 because places of R and D can be interchanged and it is multiplied with 3 because in 3 ways there are 2 letters between R and D.

So finally total arrangements= 2*3*4!=6*24=144.

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Hope this helped you.......................