Aptitude:: Permutation and Combination

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In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

A. 120 B. 720
C. 4320 D. 2160
E. None of these    

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

A. 10080 B. 4989600
C. 120960 D. None of these

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?

A. 40 B. 400
C. 5040 D. 2520

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?

A. 63 B. 90
C. 126 D. 45
E. 135    

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?

A. 32 B. 48
C. 36 D. 60
E. 120    

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