Solving Problems Involving Permutations
Solve permutation problems in Grade 9 math using nPr=n!/(n-r)! to count ordered arrangements where the sequence matters, such as race finishes, lock combinations, and seating arrangements.
Key Concepts
New Concept The number of permutations of $n$ objects taken $r$ at a time is given by the formula: $$ nP r = \frac{n!}{(n r)!} $$ What’s next Next, you’ll apply the permutation formula and related counting principles to solve problems involving arrangements, from class schedules to competition outcomes.
Common Questions
What is a permutation and when is it used?
A permutation counts the number of ordered arrangements of items where the sequence matters. Use permutations when the order is important, such as ranking 3 students from a class of 10 or arranging books on a shelf.
How do you calculate the number of permutations using the formula?
Use nPr = n! / (n-r)!, where n is the total number of items and r is the number selected. For 5P3 (selecting 3 from 5): 5! / (5-3)! = 120 / 2 = 60 arrangements.
What is the difference between a permutation and a combination?
Permutations count ordered arrangements (ABC ≠ BAC). Combinations count unordered groupings (ABC = BAC). If order matters, use permutations. If only the group selected matters, not the order, use combinations.