Question

How many words can be formed by using the letters of the word 'INSURANCE',when vowels always remain together ?

• A. $8640$
• B. $17280$
• C. $720$
• D. $None$ $of$ $these$

Answer 1

Answer: (A)

$8640$

The word is $INSURANCE$

vowels are $=IUAE$

No.of word $=$ No. of arrangements of all $9$ letters, helping the vowels together

$\underset{–}{N}\underset{–}{S}\underset{–}{R}\underset{–}{N}\underset{–}{C}\underset{–}{IUAE}$

$\Rightarrow$ No. of arrangements $=\frac{6!}{2!}\times 4!$

$6!\to$ For $6$ bundles $N,S,R,N,C$ and $\left(IUAE\right)$

$4!\to$ Arrangements of 4 vowels.

$2!\to$ For two same $N^{\prime }s$

$\Rightarrow$ No. of words $=\frac{6!\times 4!}{2}=\frac{720\times 24}{2}$

$=8640$