Out of 13 objects, 4 are indistinguishable and the rest are distinct. The number of ways we can choose 4 objects out of 13 objects is __________.

Consider an $8 \times 8$ chessboard. The number of ways 8 rooks can be placed on the board such that no two rooks are in the same row and no two are in the same column is

A rabbit is sitting at the base of a staircase which has 10 steps. It proceeds to the top of the staircase by climbing either one step at a time or two steps at a time. The number of ways it can reach the top is

The number of integers greater than 5000 and divisible by 5 that can be formed with the digits 1, 3, 5, 7, 8, 9 where no digit is repeated is

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

There are 5 parallel lines on the plane. On the same plane, there are $n$ other lines that are perpendicular to the 5 parallel lines. If the number of distinct rectangles formed by these lines is 360, what is the value of $n$?

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 _________.