Find the number of ways in which the letters of the word ARRANGE can be arranged such that both R do not come together.

Question

In how many ways the letters of the word ‘CHEKOSLOVAKIA’ can be arranged such that “SL” always comes together and ‘H’ and ‘I’ at the end places?

Answer 1

Total number of rearrangements possible = 7!/(2!×2!)
Rearrangements where the R's are together = 6!/2!
Rearrangements where R's aren't together = 7!/4 - 6!/2!
= 5040/4 - 720/2 = 900.