Six points are arranged in space so that no three are collinear.
How many line segments can be formed by joining the points in
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
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.