Question

The letters of the word ‘MEDICINE’ are

arranged in such a way that no two consonants

are together. The number of ways this can be

done is​

Answer 1

Answer:

maybe you have ans in your qousion

Answer 2

Given:

The word ‘MEDICINE’

To Find:

Arranged in such a way that no two consonants are together.

Solution:

For the given arrangements two sequences are possible

(i) consonant,vowel,consonant,vowel

(ii)vowel,consonant,vowel,consonant

Now let us first solve the first arrangement:

There are 4 consonants and 4 vowels

So

Arrangement of consonant = 4!

Arrangement of vowels =4!/2!

Now let us first solve the second arrangement:

There are 4 consonants and 4 vowels

So

Arrangement of consonant = 4!

Arrangement of vowels =4!/2!

Then,

Total number of arrangements = 2(4!×4!/2!)

                                                   = (2×4!×4!)/2×1

                                                   = 4!×4!

                                                   =576

Hence, The number of ways this can be done is 576.​