Six points are arranged in space so that no three are collinear. How many line segments can be formed by joining the points in pairs?
Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in every possible order to give 5 digit numbers. Find the sum of the resulting numbers.
Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?
30 different painted cubes.
Let the six faces be a, b, c, d, e, and f. With face a opposite face b there are six arrangements for the other four colours around the cube: cdef, cdfe, cedf, cefd, cfde and cfed. Likewise for the face a opposite face c ; face a opposite face d ; face a opposite face e ; and face a opposite face f. All have six arrangements for the remaining five colours. Hence the total is 5 x 6 = 30 arrangements.