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How many different words can be formed using all the letters o

Question

How many different words can be formed using all the letters of the word $^{'} COMB I N A T I O N^{'}$ such that the vowels as well as consonants appear in alphabetical order?

426

462

624

None of the above

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How many different words can be formed using all the letters of the word

^{'} COMB I N A T I O N^{'}

such that the vowels as well as consonants appear in alphabetical order?

15 mins ago

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15 mins ago

Text solutionVerified

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

\frac{11 !}{2 ! 2 ! 2 !}

Total no. of arrangements of consonants

= \frac{6 !}{2 !} = 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

= \frac{5 !}{2 ! 2 !} = 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

\frac{1}{360} \times \frac{1}{30} \times \frac{11 !}{2 ! 2 ! 2 !} = 462

Hence, the answer is

462.

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Question Text	How many different words can be formed using all the letters of the word $^{'} COMB I N A T I O N^{'}$ such that the vowels as well as consonants appear in alphabetical order?
Answer Type	Text solution:1
Upvotes	150

How many different words can be formed using all the letters of the word ′COMBINATION′ such that the vowels as well as consonants appear in alphabetical order?

Text solutionVerified

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How many different words can be formed using all the letters of the word $^{'} COMB I N A T I O N^{'}$ such that the vowels as well as consonants appear in alphabetical order?