The number of ways of arranging letters of the word HAVANA so that V and N do not appear together is

Step-by-step solution

We can arrange the letters H , A , A , A in 4 ! 3 ! =4 ways. If one possible arrangement is X X X X Then, we can arrange V , N at any of the two places marked with O in the following arrangement O O O O O Thus, we can arrange V and N in ^5 P₂=20 ways. Thus, the number of ways in which letters can be arranged is 4 20=80