Permutation Worksheet/Game

Permutation Worksheet/Game
Welcome to Permutation Worksheet/Game. In this game, you need to solve word problems that can be solved using the Permutation Formula. Scroll down the page for a more detailed explanation.

 

 

The Goal
Solve math word problems by finding the total number of ways to arrange a specific number of items (r) from a larger set (n).

The Rule of Permutations
Use this game when the order of items is important.
Order Matters: 1st, 2nd, and 3rd place in a race; a specific seating chart; or a President and Vice President election.
The Formula: \(P(n, r) = \frac{n!}{(n-r)!}\)
Start with the total number of items (n) and multiply by each descending number until you have filled the number of “slots” (r).

How to Play

1. Read the Mission Briefing
   A word problem will appear in the top box. Look for two key numbers:
   Total Items (n): The pool you are choosing from (e.g., 10 runners).
   Slots to Fill (r): How many are being arranged (e.g., the top 3 finishers).
   

2. Calculate the Total
   Multiply the choices for each slot. For a race with 10 runners and 3 medal spots:
   Slot 1 (Gold): 10 choices.
   Slot 2 (Silver): 9 choices left.
   Slot 3 (Bronze): 8 choices left.
   Calculation: 10 × 9 × 8 = 720.
   

3. Select Your Coordinates
   Click one of the four buttons at the bottom.
   Correct Answer: You will hear a high chime, your score increases by 10, and the “Next Mission” button appears.
   Incorrect Answer: You will hear a low buzz. A Hint Box will appear showing the specific nPr formula and its expansion (e.g., 10 × 9 × 8) to help you see where the math went wrong.
   

Quick Strategies
Read the Question:
If the problem says “elect a President and VP,” that’s 2 slots (r=2).
If it says “Gold, Silver, and Bronze,” that’s 3 slots (r=3).
No Repeats: Since these are permutations, once an item is “placed” in a slot, it cannot be used again, which is why the numbers count down.

Permutation

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