Question

How many words can be formed from the letters of the word ${}^{\prime }SIGNATUR{E}^{\prime }$ so that all the vowels come together?

• A. $17280$
• B. $4320$
• C. $720$
• D. $80$

Answer 1

The correct option is A $17280$

SIGNATURE

vowel : I,A,U,E $⟶4$

All should be together

concider all vowels to be one unit

Integral arrangement $=4!$

Rest five letter $=5$

Concider each letter as one unit

there are five units

Arrangements of these $6$ units

$\Rightarrow 6!\times 4!\Rightarrow 120\times 6\times 24\Rightarrow 2880\times 6\Rightarrow 17280$

Therefore number of words $=17280$