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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
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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