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A company has 11 software engineers and 7 civil engineers. In how many ways can they be seated in a row so that all the civil engineers do not sit together?
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How many signals can be made using 6 different coloured flags when any number of them can be hoisted at a time?
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In how many different ways can the letters of the word JUDGE be arranged such that the vowels always come together?
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A question paper has two parts P and Q, each containing 10 questions. If a student needs to choose 8 from part P and 4 from part Q, in how many ways can he do that?
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In how many different ways can the letters of the word CORPORATION be arranged so that the vowels always come together?
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In how many different ways can the letters of the word MATHEMATICS be arranged so that the vowels always come together?
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In how many different ways can the letters of the word 'RUMOUR' be arranged?
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There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
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In a chess competition involving some men and women, every player needs to play exactly one game with every other player. It was found that in 45 games, both the players were women and in 190 games, both players were men. What is the number of games in which one person was a man and other person was a woman?
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In how many ways can 11 persons be arranged in a row such that 3 particular persons should always be together?
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