1. How many permutations of 3 numbers are there? Of four? five?
There are 6 permutations of the numbers 1,2,3. These are:
1,2,3; 1,3,2; 2,1,3; 2,3,1; 3,1,2; 3,2,1.
There are 24 permutations of the numbers 1,2,3,4. These are:
1,2,3,4; 1,2,4,3; 1,3,2,4; 1,3,4,2; 1,4,2,3; 1,4,3,2;
2,1,3,4; 2,1,4,3; 2,3,1,4; 2,3,4,1; 2,4,1,3; 2,4,3,1;
3,1,2,4; 3,1,4,2; 3,2,1,4; 3,2,4,1; 3,4,1,2; 3,4,2,1;
4,1,2,3; 4,1,3,2; 4,2,1,3; 4,2,3,1; 4,3,1,2; 4,3,2,1.
There are 120 permutations of the numbers 1,2,3,4,5. These are too numerous to mention here (but see the answer to the next question)