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

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 ___

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

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

The number of ways in which coins of denominations of rupees 2, 5 and, 10 can be combined to make a value of rupees 50 is

The number of triangles that can be formed by choosing points from 7 points on a line and 5 points on another parallel line 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