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Permutations and Combinations | Word Problems

In how many ways can the letters of the word DRAUGHT be arranged, if the vowels are always kept together?
How many ways the word 'EQUATION' can be arranged so that all the vowels will always come together?
In how many ways can the leter of the word 'SCALE' be arranged, so that the vowels do not come together?
In what number of ways can the letters of the word 'ABLE' be arranged so that the vowels occupy even places?
Suppose 20 distinct points are placed randomly on a circle. Which of the following statements is/are correct? 1. The number of straight lines that can be drawn by joining any two of these points is 380. 2. The number of triangles that can be drawn by joining any three of these points is 1140. Select the correct answer using the code given below.
60 is the total number of words with or without definition which can be made using all letters of the word AGAIN. Figure-out the 49th word if these words are mentioned as in wordbook?
In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?
What is the number of words that can be formed from the letters of the word 'DAUGHTER', the vowels remaining always together?
Let n be the number of ways in which 5 men and 6 women can stand in a queue such that all the women stand consecutively. Let m be the number of ways in which the same 11 persons can stand in a queue such that exactly 5 women stand consecutively. The value of m/n is
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