I have a question that says: Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
I did this in the following way: Number of ways in which TRIANGLE can be arranged - Number of ways in which TRIANGLE can be arranged where 3 vowels are together - Number of ways in which TRIANGLE can be arranged where 2 vowels are together = 8! - (6!*3!) - (7!*2!*3) = 5760
The correct answer in my book is given to be 14400 calculated as: xTxRxNxGxLx : x depicts spaces where vowels can be arranged and they are not together. Therefore, Number of ways in which Consonants can be arranged*Number of ways in which vowels can be arranged = 5!6C33! = 14400.
Can anyone help me figure out why the method I follow isn't working?