Mathematics - Permutation Combination Question with Solution | TestHub

We can arrange the letters $\mathrm{H},\mathrm{A},\mathrm{A},\mathrm{A}$ in $\frac{4!}{3!}=4$ ways. If one possible arrangement is $$XXXX$$ Then, we can arrange $\mathrm{V},\mathrm{N}$ at any of the two places marked with $\mathrm{O}$ in the following arrangement $$\mathrm{O}\times \mathrm{O}\times \mathrm{O}\times \mathrm{O}\times \mathrm{O}$$ Thus, we can arrange $V$ and $N$ in ${}^5{P}_2=20$ ways. Thus, the number of ways in which letters can be arranged is $4\times 20=80$