Question

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

• A. 1800
• B. 600
• C. 2700
• D. 900

Answer 1

The correct option is C 2700

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 $r^{th}$ gap then the number of ways to place the 2nd A will be (7 - r - 1). So, the total number of ways = $\frac{6!}{2!2!}{\sum }_{r=1}^5(6-r)$ $=\frac{6!}{2!2!}\times (5+4+3+2+1)=2700$.