[tex] \text{Consider the word TRANCE}\\
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\text{there are total 6 letters out of which 2 are vowels A and E.}\\
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\text{now since the vowels must be together, so they can be arranged }2! \text{ ways}\\
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\text{now if we consider AE as one letter, the rest of 4 letter along with}\\
\text{AE can be arranged in }5! \text{ ways.}\\
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\text{hence the total number of arrangements with vowels always together are:}\\
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=5!\times 2!\\
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=120\times 2\\
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=240 [/tex]
Total number of arrangements= 240
