# How Many Words Can Be Formed with the Letters of the Word 'University', the Vowels Remaining Together? - Mathematics

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

Concept: Factorial N (N!) Permutations and Combinations
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.5 | Q 3 | Page 42