How many words can be formed by using the letters of the word combination so that the vowels always come together
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Given:
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
To find:
Now we have to find how many words can be formed by using the letters of the word combination so that the vowels always come together.
Solution:
Total permutations of the given word are equal to = 11! / 2!2!2!
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 = 5! / 2!2!
Only one of 30 has the alphabets in the classification A, I, I, O, O
∴ By symmetry the arrangements of given word with consonants and vowels in alphabetical order is = 1/360 * 1/30 * (11! / 2!2!2! ) = 462
Hence, the answer is 462.
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