Question

Find the number of letters from the word MAXIMUM where two consonants cannot occur. (Permutation)​

Answer 1

4!

Explanation:

In word MAXIMUM, consonants are M & X. According to the question itself, consonants should not occur together.

So, we have to put vowels at each even position; only then the 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 is 4!/3! (as repetitions of M).

Hence, the answer is 4!/3! x 3! = 24 ways.

24=4!.