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how many words are possible from the letters of the word"EXTRA",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
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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