Question

The number of permutations that can be made with the letters of the word "SRINATHDUBE", so that always a vowel occupies the central place is

• A. $10!$
• B. $4.10!$
• C. $4!.7!$
• D. $7!.10!$

Answer 1

The correct option is B $4.10!$

SRINATHDUBE
Vowels $\to$ A,E,I,U $\left(4\right)$
Consonants $\to$ B,D,H,N,R,S,T $\left(7\right)$
$\to$ The central place can be occupied by $4$ different vowels. So, the no. of ways of allocating the central place$=4$
$\to$ The other $10$ places now have $10$ option left to choose from. So, the no. of ways to choose the remaining letters $=10!$
$\to$ So, the total no. of ways $=4\times 10!$