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# Mark the correct alternative in the following: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 isA. 360B. 256C. 444D. none of these

We have, 8 objects {C}, {O}, {N}, {S}, {T}, {A}, {N}, {T} and there are 2 N's, 2 T's.

As, we are concerned about the relative positions of the vowels and consonants, so, by denoting the consonants by “×” and the vowels by “_”, we get the structure of the word as, ×_×××_××

Where, the “×” are to be filled with 6 consonants and this can be done in

= 180 ways. [as, there are 2 N's, 2 T's]

And the “_” are to be filled with 2 vowels, and this can be done in 2! = 2 ways.

As, the cases are independent, so, 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

= 360.

The discussion can be shown pictorially as:

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