Question

In how many ways can the letters of the word arrange be arranged so that neither 2 a's or 2r's are together

Answer 1

Total no of arrangements possible=7!/2!2!=1260

Total no of arrangements in which Rs are together=6!/2!=360

Total no of arrangements in which 2 As are together=6!/2!=360

Total no of arrangements in which 2 As as well as 2 R’so are together= 5!=120

Therefore total no. of arrangements in which neither 2 As nor 2 Rs are together= 1260-360-360+120=660

Answer 2

Answer:

Total no of arrangements possible=7!/2!2!=1260

Total no of arrangements in which Rs are together=6!/2!=360

Total no of arrangements in which 2 As are together=6!/2!=360

Total no of arrangements in which 2 As as well as 2 R’so are together= 5!=120

Therefore total no. of arrangements in which neither 2 As nor 2 Rs are together= 1260-360-360+120=660