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In how many ways can the letters of the word MAXIMA be arranged such that all vowels are together and all constants are together?
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Verified Answer
The correct answer is:
18
Given word $\rightarrow$ MAXIMA
Total letters $=6$
Total number of vowel $=3$, i.e. A, I, A
Total number of consonants $=3$, i.e. MXM
Number of arrangements of all vowels together
$$
\text { only }=\frac{3 !}{2 !}=3
$$
Number of arrangement of all consonants together only $=\frac{3 !}{2 !}=3$
$\therefore$ All arrangements when all vowels are together and all consonants are together
$$
\begin{aligned}
& =2 \times 3 \times 3 \\
& =18
\end{aligned}
$$
Total letters $=6$
Total number of vowel $=3$, i.e. A, I, A
Total number of consonants $=3$, i.e. MXM
Number of arrangements of all vowels together
$$
\text { only }=\frac{3 !}{2 !}=3
$$
Number of arrangement of all consonants together only $=\frac{3 !}{2 !}=3$
$\therefore$ All arrangements when all vowels are together and all consonants are together
$$
\begin{aligned}
& =2 \times 3 \times 3 \\
& =18
\end{aligned}
$$
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