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In how many ways the letters of the word...

In how many ways the letters of the word COMBINATORICS can be arranged if all vowel and all consonants are alphabetically ordered.

Text Solution

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The correct Answer is:
`.^(13)C_(5)`
Combinatorics
Vowels in alphabetical order `to` A I IO O
Consonants in alphabetical order `to` B C C M N R S T
8 places for consonant's can be selected in `.^(13)C_(8)` ways in which consonants can be arranged in one way as order of letters is fixed. Remaining 5 places can be filled by 5 vowels in one way can be filled by consonants in 1 way. Therefore,
Required numbers of arrangements `= .^(13)C_(5)`
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