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:
We know that,
nPr
$=\frac{n !}{(n-r) !}$
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