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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.

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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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