In how many ways can the letters of the word MAXIMA be arranged such that all vowels are together and all…
In how many ways can the letters of the word MAXIMA be arranged such that all vowels are together and all constants are together?
18
30
36
42
Solution
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}
$