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

Question:

How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?

Solution:

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