Question

The number of words which can be formed from the letters of the word MAXIMUM, if two consonants cannot occur together, is

• A. $4!$
• B. $3!\times 4!$
• C. $7!$
• D. None of these

Answer 1

The correct option is A

$4!$

Find the number of words which can be formed from the given word based on given information

Given word MAXIMUM has $4$ consonants and $3$ vowels.

If two consonants cannot be kept together then they must be arranged in this way

$\_A\_I\_U\_$

This arrangement can be made in $3!$ ways (permutations of A,I,U)

The $4$ consonants (3 M, 1 X) can be arranged in the $4$ blanks in $\frac{4!}{3!}$ ways

Hence, the total number of ways to arrange the letters $=3!\times \frac{4!}{3!}=4!$

Hence, there are $4!$ ways to arrange the letters of the word MAXIMUM such that no two consonants are together,

Hence option $\left(A\right)$ is correct.