Combination Worksheet/Game

Combination Worksheet/Game
Welcome to Combination Worksheet/Game. In this game, you need to solve word problems that can be solved using the Combination Formula: scenarios where you are selecting a group of items and the order doesn’t matter. Scroll down the page for a more detailed explanation.

 

 

1. Analyze the Scenario
   When a new experiment starts, read the Problem Text. Look for two specific numbers:
   n (The Pool): Shown in emerald. This is the total number of items available to choose from.
   r (The Selection): Shown in purple. This is the specific number of items you are picking for your group.
   

2. Understand the Rule
   In this game, you are dealing with Combinations. The key difference between a combination and a permutation is that in a combination, “Team A & Team B” is the same as “Team B & Team A."
   Example: Picking 2 toppings for a pizza (Pepperoni and Mushroom) is only 1 unique combination, regardless of which one you pick first.
   

3. How to Calculate
   If you are unsure of the answer, you can use the Combination Formula:
   \(\binom{n}{r} = \frac{n!}{r!(n-r)!}\)
   A quicker way to think about it (and how the game provides hints) is:
   Numerator: Multiply r decreasing numbers starting from n.
   Denominator: Divide by r factorial (r × (r-1) … × 1).
   

4. Game Controls
   Select an Answer: Click one of the four buttons at the bottom.
   Correct Answer: The button turns Emerald, your “Research Points” increase by 25, and the Next Experiment button appears.
   Incorrect Answer: The button darkens, and the Hint Box appears.
   Using the Hint: The Hint Box shows you the specific “math breakdown” for that problem. It sets up the fraction for you but leaves the final calculation with a “?” for you to solve.
   

5. Scoring
   Your goal is to accumulate as many Research Points as possible by solving the problems on your first try. If you get a question wrong, you can still find the right answer to move on, but you’ll have to use the formula expansion in the hint box to guide you.
   

Combination

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