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The numbers o...

Question

The numbers of word that can be made with all the letters of the $B H A R A T I$ so that the order of consonants and the order of vowels do not change is _____.

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Solution

The consonants can be arranged in $4! = 24$ ways
The vowels can be arranged in $\frac{3!}{2!} = 3$ ways
total no of words are $24 \times 3 = 72$

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