The total number of positive integer solutions of $21 ≤ a + b + c ≤ 25$ is

The number of solutions of the equation $x_1 + x_2 + x_3 + x_4 = 50$, where $x_1, x_2, x_3, x_4$ are integers with $x_1 \geq 1, x_2 \geq 2, x_3 \geq 0, x_4 \geq 0$ 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

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 ___

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

The number of values of $x$ for which $C \binom {17-x}{3x+1}$ is defined as an integer is

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