In how many ways can the letters of the word | vedclass

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Question

(A) The word is $MAXIMA$. Total letters $= 6$.Vowels are $\{A, I, A\}$ (Total $3$,with $A$ repeating $2$ times).Consonants are $\{M, X, M\}$ (Total $3

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(A) The word is $MAXIMA$. Total letters $= 6$.Vowels are $\{A, I, A\}$ (Total $3$,with $A$ repeating $2$ times).Consonants are $\{M, X, M\}$ (Total $3$,with $M$ repeating $2$ times).Number of ways to arrange the vowels together $= \frac{3!}{2!} = 3$.Number of ways to arrange the consonants together $= \frac{3!}{2!} = 3$.Since we have two groups (one of vowels and one of consonants),these two groups can be arranged in $2! = 2$ ways.Total number of arrangements $= 2! 	imes \left(\frac{3!}{2!}ight) 	imes \left(\frac{3!}{2!}ight) = 2 	imes 3 	imes 3 = 18$.

In how many ways can the letters of the word $MAXIMA$ be arranged such that all vowels are together and all consonants are together?

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