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6.Permutation and Combination
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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