Imagine htat each position is a box numbered from 1 to 6. You have the following
We will first find all posibilitied by simply calculating all possibilities for each box if we fill them in order.
For the first box, since we haven't chosen any player, we have 6 possibilities.
For the second box, since we have already filled box 1, we have 5 possibilites.
In the same manner, for box 3 we have 4 possibilites.
For box 4 we have 3 possibilities
For box 5 we have 2 possibilites.
Finally, for box 6 we will have only 1 possibility
So, the total number of possibilites is simply the product of all possibilites for each box
That is
[tex]6\cdot5\cdot4\cdot3\cdot2\cdot1=6!=720[/tex]so there are 720 possiblilites.
