Q. 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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Q. How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

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Q. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

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Q. In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

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Q. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

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Q. In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

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Q. How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

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Q. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

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Q. In how many ways can the letters of the word 'LEADER' be arranged?

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Q. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

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Q. 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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Q. In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

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Q. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

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