Example Card: Applying the Combination Formula
Master Applying the Combination Formula with step-by-step worked examples for Grade 9 math students. Practice identifying key patterns and apply techniques to solve problems accurately.
Key Concepts
Let's use our powerful new formula to tackle a bigger problem without listing all the possibilities. This example will show you how to apply the combination formula.
Example Problem: An ice cream shop offers 15 different toppings. How many ways can you choose 12 toppings for your sundae?
1. We need to find the number of combinations of 15 items taken 12 at a time. The formula is: $$ nC r = \frac{n!}{r!(n r)!} $$ 2. Substitute $n=15$ for the total number of toppings and $r=12$ for the number of toppings to choose. $$ {15}C {12} = \frac{15!}{12!(15 12)!} $$ 3. Simplify the expression inside the parentheses: $$ {15}C {12} = \frac{15!}{12!3!} $$ 4. To make this easier to calculate, we expand $15!$ until we reach $12!$ so we can cancel the terms. $$ \frac{15 \cdot 14 \cdot 13 \cdot 12!}{12!3!} $$ 5. Now, cancel out the $12!$ from the numerator and the denominator: $$ \frac{15 \cdot 14 \cdot 13}{3!} $$ 6. Finally, calculate the result by expanding $3!$ in the denominator. $$ \frac{15 \cdot 14 \cdot 13}{3 \cdot 2 \cdot 1} = \frac{2730}{6} = 455 $$ There are 455 ways to choose 12 toppings from 15.
Common Questions
What is Applying the Combination Formula in Grade 9 math?
Applying the Combination Formula is a key algebra concept where students learn to apply mathematical rules and properties to solve problems. Understanding this topic builds skills needed for higher-level math.
How do you solve problems involving Applying the Combination Formula?
Identify the given information, apply the relevant property or formula, simplify step by step, and check your answer. Practice with varied examples to build fluency.
Where is Applying the Combination Formula used in real life?
Applying the Combination Formula appears in fields like science, engineering, finance, and technology. Understanding this concept helps solve real-world problems that involve mathematical relationships.