The number of ways of arranging the letters of the word EQUATION so that the order of the vowels and the order of the consonants is not changed is

^{8} C_{3} . 8!

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^{8} C_{3}

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^{8} P_{3}

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^{8} P_{3} 6!

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Solution

The correct option is C $^{8} C_{3}$
AEUOI : QTN;
Select any $3$ places for consonants from $8$ places in $^{8} C_{3}$ ways.
Arrangement can be done only in $1$ way and we can arrange $5$ vowels in order $1$ way only
Hence, required number of ways is $=^{8} C_{3}$

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In how many ways can the letters of the word 'ALGEBRA'be arranged without changing the relative order of the vowels and consonants ?

In how many ways can the letters of the word 'INTERMEDIATE' be arranged so that :

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" T R I A N G L E "

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