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# How many words with or without meaning can be formed with letters of the word EQUATION at a time so that vowels and consonants occur together?

$\begin{array}{1 1}(A)\;1000\\(B)\;1430\\(C)\;1440\\(D)\;1560\end{array}$

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• $n!=n(n-1)(n-2)......(3)(2)(1)$
The word EQUATION consists of 5 vowels and 3 consonants.
5 words can be arranged in 5!
$5!=5\times 4\times 3\times 2\times 1$
$\;\;\;\;=120$ ways
3 consonants can be arranged in 3!
$3!=3\times 2\times 1$
$\;\;\;\;=6$ ways
The two block of vowels and consonants can be arranged in 2! ways
$2!=2\times 1$
$\;\;\;\;=2$ ways
$\therefore$ The number of words which can be formed with letters of the word EQUATION so that vowels and consonants occur together
$\Rightarrow 120\times 6\times 2$
$\Rightarrow 1440$
Hence (C) is the correct answer.

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