Given:

The word \[UNIVERSITY\]

There are \[10\] letters in the word \[UNIVERSITY\] out of which \[2\text{ }are\text{ }Is\]

There are \[4\]vowels in the word \[UNIVERSITY\] out of which \[2\text{ }are\text{ }Is\]

So these vowels can be put together in \[n!/\text{ }\left( p!\text{ }\times \text{ }q!\text{ }\times \text{ }r! \right)\text{ }=\text{ }4!\text{ }/\text{ }2!\] Ways

Let us consider these \[4\] vowels as one letter, remaining \[7\] letters can be arranged in \[7!\] Ways.

Hence, the required number of arrangements \[=\text{ }\left( 4!\text{ }/\text{ }2! \right)\text{ }\times \text{ }7!\]

\[=\text{ }\left( 4\times 3\times 2\times 1\times 7\times 6\times 5\times 4\times 3\times 2\times 1 \right)\text{ }/\text{ }\left( 2\times 1 \right)\]

Or,

\[=\text{ }4\times 3\times 2\times 1\times 7\times 6\times 5\times 4\times 3\]

\[=\text{ }60480\]