Permutations and Combinations Exam Pattern Mix

The 8 corners of a cube are joined in pairs by straight segments. How many of these segments are neither edges nor diagonals of a face?

Eight points are marked at equal spacing on a circle.

How many chords can be drawn joining pairs of these points?

Eight points are marked at equal spacing on a circle.

How many quadrilaterals have all four corners among these points?

There are 4 routes from A to B, 3 from B to C, and 2 direct routes from A to C. In how many ways can one travel from A to C?

In how many ways can the digits 1 to 9 be arranged so that the odd digits occupy the odd positions?