Question

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

• A. $7200$
• B. $36000$
• C. $14400$
• D. $1240$

Answer 1

Answer: (C)

TRIANGLE
Number of consonants $=5(T,R,N,G,L)$
$X\cdot X\cdot X\cdot X\cdot X\cdot X$
Vowels $=3(A,E,I)$
Place consonants at dot places. This can be done in $5!=120$ ways.
Number of cross places $=6$
If we place vowels at these places, then no two vowels are together.
This can be done in ${}^6{P}_3$ ways $=6\times 5\times 4=120$ ways
$\therefore$ reqd. number of ways $=120\times 120$
$=14400$.