Question

5. How many different words can be formed with the letters of word 'UNIVERSITY'so that all
the vowels occur together?
​

Answer 1

Answer:

60480

Step-by-step explanation:

Given as

The word ‘UNIVERSITY’ Here's 10 letters in the word ‘UNIVERSITY’ out of which 2 are I’s

Here's are 4 vowels in the word ‘UNIVERSITY’ out of which 2 are I’s

Therefore these vowels can be put together in n!/ (p! × q! × r!) = 4! / 2! Ways

Now, let us consider these 4 vowels as one letter, remaining 7 letters can be arranged in 7! Ways.

Thus, the required number of arrangements = (4! / 2!) × 7!

= (4 × 3 × 2 × 1 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (2 × 1)

= 4 × 3 × 2 × 1 × 7 × 6 × 5 × 4 × 3

= 60480