Select three of five distinct objects without repetition.
Does changing their order make a new outcome?
Predict both counts. Take eight seconds to think.
[Eight-second silent thinking pause. The authored prompt remains visible; no native result has appeared.]
Open Course modules, then Counting and sample spaces.
The module opens with its own defaults: three objects and two selections.
Set the number of distinct objects to five.
Then set the number selected to three.
The labels one through five stand for our source letters A through E.
Ordered without replacement treats each different order as a different outcome.
Within each selection, every object can appear at most once.
The native result is sixty ordered selections.
The module lists all sixty ordered triples; each has three different labels.
Keep five and three. Change the experiment to unordered without replacement.
Different orders of the same selection now count as one group.
The native result is ten unordered groups.
The probability columns use the module's stated drawing model.
For ordered selections, multiply five times four times three. The count is sixty.
One three-object group has six orders: three factorial equals six.
Divide sixty by six to count each group once. There are ten groups.
For this example, use distinct objects and no repetition.