Number of words not starting and ending with vowels formed, using all letters of word 'UNIVERSIT

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Gujarati

Hindi

6.Permutation and Combination

normal

The number of words not starting and ending with vowels formed, using all the letters of the word $'UNIVERSITY'$ such that all vowels are in alphabetical order, is

A

${}^8{C_4}.6!$

B

${}^8{C_4}.8!$

C

${}^8{C_6}.6!$

D

${}^8{C_4}.7!$

Solution

Total words not starting and ending in vowels,

but having vowels in alphabetical order

$ = \,\left( {^6{{\rm{C}}_2} \times 2!} \right) \times {\,^8}{{\rm{C}}_4} \times 4! = {\,^8}{{\rm{C}}_4} \cdot 6!$

Standard 11

Mathematics

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