Question

[10 points] Find the number of ways of arranging the letters of EQUATION, so that all the vowels are in alphabetical order.

Answer 1

Answer: The number of ways of arranging the letters of EQUATION, so that all the vowels are in alphabetical order = 336 .

Explanation:

Given word = "EQUATION"

Total letters = 8

Total Vowels (EUAIO)=5

Total number of ways to arrage letters = 8!

Number of ways to arrange vowels in alphabetical order = 5!

Then, The number of ways that all the vowels are in alphabetical order will be :

`(8!)/(5!)=(8*7*6*5!)/(5!)=336`

Hence, the number of ways of arranging the letters of EQUATION, so that all the vowels are in alphabetical order = 336 .