Question

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

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

Answer 1

Answer: (C)

$14400$

Answer 2

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 $= 120\times120$ $=14400$.