Find the number of different words


 Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together.


We know that,


$=\frac{n !}{(n-r) !}$

According to the question,

Total number of vowels letter =3,


Total number of consonants letter =5

The vowels can be placed in

6P3 = 6!/3! = 120

The number of way consonants can be arranged placed =5! =120

Therefore, total number of ways it can be arranged =5!×6P3=120×120 =14400

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