There are 10 points in the plane, of which 5 points are collinear and no three among the remaining are collinear. Then the number of distinct straight lines that can be formed out of these 10 points is

Let $n$ be the number of ways in which 20 identical balloons can be distributed among 5 girls and 3 boys such that everyone gets at least one balloon and no girl gets fewer balloons than a boy does. Then

In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together?

The number of 5-digit numbers consisting of distinct digits that can be formed such that only odd digits occur at odd places is

The number of ways in which three distinct integers can be chosen from the set $\{1, 2, \ldots, 9\}$ such that their product is divisible by 4, is ___

If 5 boys and 3 girls sit randomly around a circular table, the probability that there will be at least one boy sitting between any two girls is

How many different numbers can be formed by using only the digits 1 and 3 which are smaller than 3000000?