Question

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

• A. 40
• B. 60
• C. 80
• D. 100

Hint:

When solving problems involving restrictions on arrangements, calculate the total number of unrestricted arrangements and subtract the number of arrangements where the restriction is violated.

Answer 1

The Correct Option is C

We can arrange the letters \(H, A, A, A\) in \(\frac{4!}{3!} = 4\) ways. 
If one possible arrangement is \(XXXX\), then, we can arrange \(V\) and \(N\) at any of the two places marked with \(0\) in the following arrangement: \[ 0 \times 0 \times 0 \times 0 \times 0 \] Thus, we can arrange \(V\) and \(N\) in \(5P_2 = 20\) ways. Therefore, the total number of ways in which letters can be arranged is \(4 \times 20 = 80\).