Question

How many words can be formed from the letters of the word DOGMATIC, if all the vowels remain together :

• A. 4140
• B. 4320
• C. 432
• D. 43

Answer 1

Answer: (B)

4320

Answer 2

Total numbers of letters in the given word = 8 Total no. of 8 letters word formed = P (8, 8) = 8! No. of vowels = 3 (i.e., O, A, I) If we consider these three vowels as one letter, then the number of different words = 8 - 3 = 5 + 1 (as 3?? vowels are considered as 1 word) Hence, the total number of 8 letters in which vowel remains together = P (3 $\times$ 3) $\times$ P (6 $\times$ 6) = 3! $\times$ 6! = 6 $\times$ 720 = 4320