how many words are possible from the letters of the wordEXTRA,such that no vowel repeates?

total number of ways of arrangement ==> 5 5 5 5 5 ==> 5⁵

number of ways in which vowels are repeated

since there are 2 vowels... and 3 words apart from the vowels...

Case 1:- 2 vowel 3 others

2 2 3 3 3

Case 2:- 3 vowel 2 others

2 2 2 3 3

Case 3:- 4 vowel 1 other

2 2 2 2 3

Case 4:- 5 vowels

2 2 2 2 2

No of ways in which vowel is not repeated ==> total number of ways - no of repeititions..

==> 3125-108-72-48-32

==>2865

Approved