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

Step-by-step solution

Given word 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 only = 3 ! 2 ! =3 Number of arrangement of all consonants together only = 3 ! 2 ! =3 All arrangements when all vowels are together and all consonants are together aligned & =2 3 3 & =18 aligned