Question

How many combination of letters can be formed using all the letters of
the word 'COALSHED' so that the vowels are always together?
SE​

Answer 1

Explanation:

Given letters C,O,O,M,B,I,I,N,N,A,T

Consonants −C,M,B,N,N,T=6 letters

Vowels −O,O,I,I,A=5 letters

Total permutations of the given word is equal to

2!2!2!

11!

Total no. of arrangements of consonants =

2!

6!

=360

Out of these 360 ways , only one way has the alphabets in the order B,C,M,N,N,T ( alphabetical )

Similarily for vowels total =

2!2!

5!

=30

Only one of 30 has the alphabets in the order A,I,I,O,O

∴ By symmetry the arrangements of given word with consonants and vowels in alphabetical order is

360

1

×

30

1

×

2!2!2!

11!

=462

Hence, the answer is 462.