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Question
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
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Solution
Total number of words in ‘TRIANGLE’ = 8
Out of 5 are consonants and 3 are vowels
If vowels are not together, taken we have the following arrangement
V | C | V | C | V | C | V | C | V | C | V
Consonant can be arranged in 5! = 120 ways
Vowel occupy 6 places
∴ 3 vowels can be arranged in 6 places = 6P3
= `(6!)/((6 - 3)!)`
= `(6!)/(3!)`
= 120 ways
So, the total arrangement = 120 × 120 = 14400 ways
Here, the required arrangement = 14400 ways.
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