Question

in how many ways can six players be assigned to six positions on a baseball team assuring there any player can play any position

Answer 1

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

`6\cdot5\cdot4\cdot3\cdot2\cdot1=6!=720`

so there are 720 possiblilites.