How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by