In how many ways the letters of the word '"excellent"' can be arranged so that the vowels are always together?
Answers
Total no of letter = 9
E is repeated 3 times
L is repeated 2 times
Total no if arrangement = 9!/3! × 2!
= 362880/ 12
= 30240
So there are 30240 ways are for the arrangement of word ' Excellent '
Given,
Word excellent
To find,
number of ways in which this word can be arranged
Solution,
total no. of letters = 9
L is repeated = 2 times
E is repeated = 3 time
but according to the question, if the vowel letter (3E) always comes together then 3E is considered as 1 letter
then the remaining total letter (n)= 6+1
the total arrangement in which 3E always comes together =7!/(2)
=2520 Ways
Thus, the number of ways in which the given word can be arranged keeping in mind the condition is 2520