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

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

Grade:12th pass

1 Answers

Ritvik Gautam
85 Points
11 years ago

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

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