Home
Class 11
MATHS
Find the number of different words that ...

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

A

12000

B

14400

C

13590

D

11100

Text Solution

Verified by Experts

The correct Answer is:
B
Number of letters in the word 'TRIANGLE', = 8, out of which 5 are consonants and 3 are vowels.
If vowels are not together, then we have following arrangement.
`{:(V, C, V, C, V, C, V, C, V, C, V):}`
Consonants can be arranged in `= 5"!" = 120` ways and vowels can occupy at 6 places.
The 3 vowels can be arranged at 6 place in `""^(6)P_(3)` ways `= (6"!")/(6 - 3"!") = (6"!")/(3"!")`
`= (6 xx 5 xx 4 xx 3"!")/(3"!") = 120`
Total number of arrangement ` = 120 xx 120 = 14400`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    NCERT EXEMPLAR ENGLISH|Exercise Long Answer Type Questions|6 Videos

  • PERMUTATIONS AND COMBINATIONS

    NCERT EXEMPLAR ENGLISH|Exercise Objective Type Questions|15 Videos

  • MATHEMATICAL REASONING

    NCERT EXEMPLAR ENGLISH|Exercise OBJECTIVE TYPE QUESTIONS|21 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    NCERT EXEMPLAR ENGLISH|Exercise OBJECTIVE TYPE QUESTIONS|5 Videos

Similar Questions

Explore conceptually related problems

The number of different words that can be formed from the letters of the word 'PENCIL', so that no two vowels are together, is

The number of different words that can be formed from the letters of the word ‘INTERMEDIATE’ such that two vowels never come together is ________.

How many different words can be formed of the letters of the word 'MALKENKOV' so that no two values are together

Find the number of different words formed with the letters of the word HARYANA.

How many diferent words can be formed with the letters of the word VICE-CHANCELLOR so that the vowels are together?

How many different words can be formed with the letters of the word CLIFTON.

Find the number of seven letter words that can be formed by using the letters of the word SUCCESS so that the two C are together but no two S are together.

Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that(i) all vowels occur together (ii) all vowels do not occur together.

Number of different words that can be formed using all the letters of the word 'DEEPMALA' if two vowels are together and the other two are also together but separated from the fist two is

The number of different words that can be formed using all the letters of the word 'SHASHANK' such that in any word the vowels are separated by atleast two consonants, is