If all the letters of the word ARRANGE are arranged in all possible ways , in how many of words we will have the A`s not together and also the R`s not together?

Total no of arrangements possible=7!/2!2!=1260Total no of arrangements in which Rs are together=6!/2!=360Total no of arrangements in which 2 As are together=6!/2!=360Total no of arrangements in which 2 As as well as 2 R’so are together= 5!=120Therefore total no. of arrangements in which neither 2 As nor 2 Rs are together= 1260-360-360+120=660