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Question
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
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Solution
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is 151200.
Explanation:
Total number of words is INTERMEDIATE = 12
Which have 6 vowels and 6 consonants
If two vowels never come together then we can arrange as under
V C V C V C V C V C V C V
Here, vowels are IEEIAE where 2 I’s and 3 E’s are there.
∴ Number of ways of arranging vowels = `(7!)/(3!2!)` = 420.
Consonants are NTRMDT where 2T’s are there
∴ Number of ways arranging consonants = `(6!)/(2!)`
= `(6*5*4*3*2!)/(21)` = 360
So, the total number of words are = 420 × 360
= 151200
Hence, the value of the filler is 151200.
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