The number of different words that can be formed using all the letters of the word 'SHASHANK' such that in any word the vowels are separated by atleast two consonants, is

Options

A. `2700`
B. `1800`
C. `900`
D. `600`

Answer

A

Explanation

`(a)` The letters other than vowels are `SHSHNK` which can be arranged in `(6!)/(2!2!)` ways.
Now in its each case, let the first `A` be placed in the `r^(th)` gap. Then the number of ways to place the `2nd A` will be `(7-r-1)`. So, the total number of ways `=(6!)/(2!2!)sum_(r=1)^(5)(6-r)`
`=(6!)/(2!2!)xx(5+4+3+2+1)`
`=2700`