Solution
Find all the possible scenarios where vowels come together and subtract it from the total words possible
The word LETTER has 6 alphabets of which 2 are repeated twice.
The total number of 6 letter words =6!2!2!=6×5×4×3×22×2
=180 words
There are 2 vowels in the word LETTER, that is, (EE).
If EE are assumed to be together they can be arranged in 5!2! ways.
So, the words where vowels are together are 5!2!=1202=60
Thus, the total number of words where vowels are not together=180-60=120
Hence, there are 120 words formed from the word LETTER where no vowels are together.
In how many different ways can the letters of the word EXTRA be arranged so that the vowels are never together?
A. 120
B. 48
C. 72
D. 168
E. None of these
Answer: Option C
Solution(By Examveda Team)
Taking the vowels (EA) as one letter, the given word has the letters XTR (EA), i.e., 4 letters.
These letters
can be arranged in 4! = 24 ways
The letters EA may be arranged amongst themselves in 2 ways.
Number of arrangements having vowels together = (24 × 2) = 48 ways
Total arrangements of all letters
= 5!
= (5 × 4 × 3 × 2 × 1)
= 120
Number of arrangements not having vowels together
= (120 - 48)
= 72
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