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

Answer 1

Hey there !!

R_ _ D_ _
_R_ _ D_
_ _ R_ _ D  these are the different arrangements in which R and D have two letters between them. These 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.

Hope this helped you !!