Thank you for reporting, we will resolve it shortly
Q.
The number of different words that can be formed from the letters of the word 'TRIANGLE so that no vowels are together is :
Permutations and Combinations
Solution:
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 $=6\times5\times4=120$ ways
$\therefore $ reqd. number of ways $= 120\times120$
$=14400$.