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

Options

A. 12000
B. 14400
C. 13590
D. 11100

Answer

B

Explanation

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`