How many words can be formed with the letters of the word 'UNIVERSITY',

The word UNIVERSITY consists of 10 letters that include four vowels of which two are same.

Thus, the vowels can be arranged amongst themselves in $\frac{4 !}{2 !}$ ways.

Keeping the vowels as a single entity, we are left with 7 letters, which can be arranged in 7! ways.

By fundamental principle of counting, we get,

Number of words $=7 ! \times \frac{4 !}{2 !}=60480$