Find the number of ways of arranging the letters of the word TRIANGLE

1.	Find the number of ways of arranging the letters of the word TRIANGLE so that the relative positions of the vowels and consonants are not disturbed.
Answer» In a given, word, [Hint : Vowels – A, E, I, O U] number of vowels is 3 number of consonants is 5 C C V V C C C V Since the relative positions of the vowels and consonants are not disturbed, the 3 vowels can be arranged in their relative positions in 3! ways and the 5 consonants can be arranged in their relative positions in 5! ways. ∴ The number of required arrangements = (3!) (5!) = (6) (120) = 720.

Find the number of ways of arranging the letters of the word TRIANGLE so that the relative positions of the vowels and consonants are not disturbed.

Answer»

In a given, word, [Hint : Vowels – A, E, I, O U]

number of vowels is 3

number of consonants is 5

C C V V C C C V

Since the relative positions of the vowels and consonants are not disturbed, the 3 vowels can be arranged in their relative positions in 3! ways and the 5 consonants can be arranged in their relative positions in 5! ways.

∴ The number of required arrangements = (3!) (5!) = (6) (120) = 720.

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Find the number of ways of arranging the letters of the word TRIANGLE so that the relative positions of the vowels and consonants are not disturbed.

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