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Answer»

Given word is 'GLOOMY'.

There are 6 letters in GLOOMY with 4 distinct letters and 2 O's.

These letters can be ARRANGED in (6!/2!) = 360.

(i)

Given that two O's should not be together.

Let us consider 2 O's as ONE LETTER and thus there will be 5 distinct letters. These 5 distinct letters can be arranged in 5! ways. = 5! = 5*4*3*2*1 = 120.


Therefore, Required number of ways = 360 - 120

⇒ 240.



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