QuestionConsider the arrangement of all letters of word MOTALE. Then
One/More correct answer(s) A. Number of arrangements in which vowels and consonants are alternate is $2.3!3$ ! B. Number of arrangements in which vowels are alternate is $3!3$ ! C. Number of arrangements in which consonants come before vowels is 3 ! 3 ! D. Number of arrangements in which vowels are in alphabetical order is $\frac{6!}{3!}$

Studdy Solution
For vowels to be in alphabetical order, fix the order of vowels as A, E, O.
- The number of ways to arrange the consonants is $3!$.
Thus, the total number of arrangements is $3!$.
Now, let's evaluate each option:
A. Number of arrangements in which vowels and consonants are alternate is $2 \times 3! \times 3!$. This is correct. B. Number of arrangements in which vowels are alternate is $2 \times 3! \times 3!$. This is correct. C. Number of arrangements in which consonants come before vowels is $3! \times 3!$. This is correct. D. Number of arrangements in which vowels are in alphabetical order is $3!$. This is incorrect; it should be $3!$, not $\frac{6!}{3!}$.
Correct answers: A, B, C.