Permutations
Count arrangements after checking order and repetition conditions.
Meaning
Permutations arrange distinct objects with order taken into account. Choosing the same objects in a different order counts as a different result.
Example
Choosing a president and vice president from 4 different students gives 4 choices for president and 3 for vice president, for 12 possibilities. With one student unable to hold both offices, choosing the president leaves three candidates. Each president can be paired with any of those three vice presidents, giving 4×3=12. Swapping offices makes a different outcome. Do not directly use permutations when the selected positions have indistinguishable roles. Also check whether repetition is allowed and whether rotations count as the same circular arrangement.
Practice for this concept
Scope and references
Topics
Ordered arrangements, factorials, arrangements with repetition, repeated objects, circular permutations
Learning goal
Count arrangements after checking order and repetition conditions.
Helpful background
Review systematic counting and conditions on order and repetition.
Permutations
These choice exercises calculate or judge specified finite data, trials, or assumptions. They do not establish data collection, written inference, model validation, or mastery of the whole statistics area.