Find the number of ways of arranging the letters of the word $" T R I A N G L E "$ so that the relative positions of the vowels and consonants are not disturbed.

Open in App

Solution

Vowels $: A, E, I, O, U$

In the word $" T R I A N G L E "$
$\Rightarrow$ Number of vowels $= 3$
Number of constants $= 5$

Since the relative positions of the vowels and consonants are not distributed. The $3$ volumes 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 $= (3!) (5!) = (6) (125) = 720$ ways.
Hence, the answer is $720.$

Suggest Corrections

Similar questions

Q. Find the number of ways of permuting the letters of the word

P I C T U R E

so that
(i) All vowels come together
(ii) No two vowels come together
(iii) The relative positions of vowels and consonants are not disturbed

Q. In how many ways the letters of the word

^{'} C O R P O R A T I O N^{'}

can be arranged so that the relative positions of vowels and consonants is not changed.

Q. The letters of the word

^{'} L O G A R I T H M^{'}

are arranged in all possible ways. The number of arrangements in which the relative positions of the vowels and consonants are not changed is

Q. The letters of the word

^{'} L O G A R I T H M^{'}

are arranged in all possible ways. The number of arrangements in which the relative positions of the vowels and consonants are not changed is

Find the number of ways in which the letters of the word EXCAVATION be rearranged so that the relative position of the vowels and consonants remain the same.

Join BYJU'S Learning Program

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.

Find the number of ways of arranging the letters of the word $" T R I A N G L E "$ so that the relative positions of the vowels and consonants are not disturbed.