# The number of arrangements of the letters of the word ′VEER BHADUR′in which two vowels are together and other two vowels are together but separated from each other-

$\\\text{VEER BHADUR }\\ (\mathrm{EE})(\mathrm{AU}) and \\ (EU) (AE) are the only pair of Vowels possible. VRBHDR can be arranged in \frac{6 !}{2} ways (\mathrm{R} is repeated )-\ldots-(1) \\ The vowel pairs can be placed in between the spaces \\ of the alphabets from (1) \\ For (EE) (AU) \rightarrow 2 arrangements \\ (EU) (AE) \rightarrow 4 arrangements \\ Number of arrangements$

$\large \begin{array}{l} =\frac{6 !}{2}\left[7 p_{2} \times 2+7 p_{2} \times 4\right] \\\\ =\frac{6 !}{2}[84+168] \\\\ =\frac{7 !}{2}[12+24]=\frac{36 \times 7 !}{2} \\\\ =18 \times 7 ! \text { ways. } \end{array}$

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