# In how many ways can the letters of the word “INTERMEDIATE” be arranged so that :i. the vowels always occupy even places?ii. the relative order of vowels and consonants do not alter?

Given the word INTERMEDIATE. IT has 12 words out of which 6 are vowels, and 6 of them are consonants.

(i) the vowels always occupy even places?

i.e., There are 6 vowels, and there can occupy even places, i.e. position number 2, 4, 6, 8, 10, and 12.

A number of ways of arranging 6 vowels among 6 places = 6!/(2! x 3!)

(Since there are 2 repeating vowels I (twice) and E (thrice)).

A number of ways of arranging 6 consonants among 6 places = 6! / 2!

(Since there are 1 repeating consonant T repeating twice).

Total number of ways of arranging vowels and consonants such that vowels can occupy only even positions

= 21600

Hence, a number of ways of arranging INTERMEDIATE’s letters such that vowels can occupy only even positions is equals to 21600.

(ii) The relative order of vowels and consonants does not alter?

A number of ways of arranging vowels = 6! / (2! x 3!)

A number of ways of arranging consonants = 6! / 2!

Total number of ways of arranging the letter of word INTERMEDIATE such that the relative order of vowels and consonants does not alter

= 21600

Hence, a total number of ways of arranging the letters of the word INTERMEDIATE such that the relative orders of vowels and consonants do not change is 21600.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Circular permutations61 mins
Challenging Quiz on P&C | Test Yourself55 mins
Permutations & Combinations | Analyze your learningFREE Class
Understand Permutations like never before60 mins
Check Your progress Part 2| Interactive Quiz: Permutation & CombinationFREE Class
Interactive Quiz on Combinations-0253 mins
Interactive Quiz on Combinations50 mins
Division and distribution of objects58 mins
Lecture on Combinations49 mins
Interactive Quiz on Division and distribution of objects17 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses