$\begin{array}{1 1}(A)\;1440\\(B)\;144\\(C)\;7!\\(D)\;4C_4\times 3C_3\end{array} $

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- $C(n,r)=\large\frac{n!}{r!(n-r)!}$
- $n!=n(n-1)(n-2)(n-3)......(3)(2)(1)$

In word ARTICLE.There are 3 vowels and 4 consonants

Total no of letters =7

Total no of even place =3

There are 3 vowels to be filled in 3 places

Hence the no of ways =$3C_3=1$

The vowels can arrange among themselves in 3! ways

$\Rightarrow 6$

Now the four consonants can fill the remaining 4 places in =4!

$\Rightarrow 4\times 3\times 2\times 1$

$\Rightarrow 24$

The total no of words formed =$1\times 6\times 24$

$\Rightarrow 144$ ways

Hence (B) is the correct answer.

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