Question: 1. How many ways are there of arranging 16 football teams into four groups of four?
2. A class contains 30 pupils. For a chemistry project, the class is to be put into four groups, two of size 7 and two of size 8. In how many ways can this be done?
3. In the early versions of the Enigma ma chine, used in Germany in the 1930s, the plugboard swapped six pairs of distinct letters of the alphabet . In how many ways can this be done (assuming 26 letters)?