Question

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

• A. $4!$
• B. $3!\times 4!$
• C. $3!$
• D. $\frac{4!}{3!}$

Answer 1

Answer: (A)

$4!$

In word MAXIMUM, consonants are M & X. According to question $2$ consonants shouldn't occur together.

So, we have to put vowels at each even position, then only our condition will be satisfied.

We can put this in $3!$ ways (permutations of A, I & U)

For odd positions we can put $3$-M's & a X. Total ways $\frac{4!}{3!}$ (as repetitions of M).

So answer is $\frac{4!}{3!}\times 3!=24$ ways

Answer: $4!$.