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The number of arrangements that can be made by using all the letters of the word PREETHI so that vowels may be in the even places is $N,$ then $\sqrt{N + 9} =$ ______

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answer is 9.

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Detailed Solution

$\begin{matrix} - & - & - & - & - & - & - \\ 1 & 2 & 3 & 4 & 5 & 6 & 7 \end{matrix}$

Arrange $' 3'$ vowels in $' 3'$ spaces in $\frac{3!}{2!}$ ways

Arrange 4 consonants in 4! Ways

Total number of ways $= \frac{3!}{2!} \times 4! = 3 \times 4!$

$\sqrt{3 \times 4! + 9} = \sqrt{81} = 9$

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