Mathematics - Permutation & Combination Question with Solution | TestHub

The letters other than vowels are SHSHNK which can be arranged in $\frac{6!}{2!2!}$ ways. Now in its each case, let the first A be placed in the $r^{t}h$ gap then the number of ways to place the 2ⁿᵈ A will be ($7-r-1$). So, the total number of ways $=\frac{6!}{2!2!}{\sum }_{r=1}^5(6-r)$

$$=\frac{6!}{2!2!}\times (5+4+3+2+1)=2700.$$