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Question
The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is
Options
360
256
444
none of these.
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Solution
360
The word CONSTANT consists of two vowels that are placed at the 2nd and 6th position, and six consonants.
The two vowels can be arranged at their respective places, i.e. 2nd and 6th place, in 2! ways.
The remaining 6 consonants can be arranged at their respective places in \[\frac{6!}{2!2!}\]ways.
∴ Total number of arrangements =\[2! \times \frac{6!}{2!2!}\]
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