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. $Noneofthese$

Answer 1

The correct option is A $4!$

Constants are M,M,X,M vowels are A,I,U

Let constants be denoted by 'C' and vowel by'V' required arrangement is

$C\underset{–}{V}C\underset{–}{V}C\underset{–}{V}C$

Constants can be arranged is $\frac{4!}{3!}$ ways

And vowels in $3!$ ways

$\therefore$ Total no. of arrangement $=\frac{4!}{3!}\times 3!$ ways

$=4!=4\times 3\times 2\times 1=24$ ways