To do this you would use a ! function in your calculator. In short this takes any number and multiplies it by all the number beneath it. In this case it would say 5 x 4 x 3 x 2 x 1. You arrange it this way because they're are five different people in spot on, but once spot one is taken there are only 4 people left for spot two and so on. So, the answer to this would be 120 different combinations.
The reasoning is the following: To select the first student, you have 5 options. For the second, whichever you chose for the first student, you have 4 options... etc.
There are 5040 ways.
7
20*19*18*17*16 = 1860480 ways.
720
27!
There are 5040 ways.
7
20*19*18*17*16 = 1860480 ways.
This is a question of permutation. There are only 3 ways. A-B-C, B-C-A, C-A-B
for the first student in the line there are 10 choices, then for the second 9 choices left, for the third 8 choices left and so on... So it's 10x9x8x7x6x5x4x3x2x1 = 3628800
720
3 items (or people) can line up in 6 different sequences. 6 items (or people) can line up in 720 different sequences.
6 = 3*2*1
5x4x3x2x1=120
25
If you keep them in a line, there are 24 ways to line them up. Then of course there are squares, diamonds, rectangles, parallelograms, stacks, etc.
-- The first place can be any one of 20 students. For each of these, -- the second place can be any one of the remaining 19 students. For each of these, -- the third place can be any one of the remaining 18 students. For each of these, -- the fourth place can be any one of the remaining 17 students. So the four places can be assigned in any one of (20 x 19 x 18 x 17) = 116,280 ways.