Question

Anagrams are made by using the letters of the word ${}^{\prime }HINDUSTA{N}^{\prime }$ In how many of these anagrams all the vowels come together?

Answer 1

$HINDUSTAN$

Number of letters $=9$

Number of vowels $=3$

Number of consonants $=6$

Concider the vowels to be one entity with $3!$ (internal arrangements )

Total number of entities $=7$

Therefore total number of arrangements

$=\frac{7!}{2!}\times 3!=15120$

Vowels come together in $15120$ Ways

Answer $15120$