$\begin{array}{1 1}(A)\;14300\\(B)\;14200\\(C)\;14400\\(D)\;14500\end{array} $

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

Given

TRIANGLE

Total no of vowels =3

Total no of consonants =5

The vowels can be placed in $\rightarrow 6P_3$

$\Rightarrow \large\frac{6!}{3!}$

$\Rightarrow \large\frac{6\times 5 \times 4\times 3!}{3!}$

$\Rightarrow 120$ ways

The consonants can be placed in their places in 5!

$\Rightarrow 5\times 4\times 3\times 2\times 1$

$\Rightarrow 120$ways

Total no of ways =$120\times 120$

$\Rightarrow 14400$ ways

Hence (C) is the correct answer.

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