Predict the result
Eight swimmers compete. How many podium orders and complete finishing orders are possible?
A swimmer cannot fill two places.

Set up the model
There are eight choices for first place, then seven for second.
Six swimmers remain for third place.

Work the example
Eight times seven times six gives three hundred thirty-six podium orders.
For a full finish, continue multiplying down to one.
Eight factorial equals forty thousand three hundred twenty.
These are different ordered arrangements.

Check the result
Now count the different orders of five distinct cards.
Take eight seconds to think before the answer appears.
[Eight-second silent pause to work; the answer remains hidden.]
Five factorial is five times four times three times two times one.
There are one hundred twenty orders.

Interpret the result
Use decreasing counts when choices cannot be reused.
Use the original task and check that your result fits its meaning.