The number of ways in which the letters of the word ‘CONSTANT’
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

(a) 360

(b) 256

(c) 444

(d) none of these.

Solution:

(a) 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.

$\therefore$ Total number of arrangements $=2 ! \times \frac{6 !}{2 ! 2 !}=360$

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