Lesson 2D: Combinations
| The word combination is often misused in day-to-day language. In fact, the words combination and permutation , which you learned about in Lesson 2C, are often used interchangeably. There is a difference. |
|
Consider the following statement: The combination to my bike lock is 1968 .
|
|
The word combination is misused in this statement because you cannot enter in 1698, 8916, or 9618 to open the bike lock successfully.
In this case, order does matter!
The correct statement is The permutation to my bike lock is 1968 . |
Look at another scenario.
|
The girl in this picture is eating a salad made of lettuce, tomatoes, yellow peppers, and red peppers. Are the foods that make up her salad a combination or permutation? The order of the food does not matter and the order does not change the salad. The group of food is a combination. The correct statement is Her salad is a combination of lettuce, tomatoes, yellow peppers, and red peppers . |
|
In this Training Camp , you will investigate combinations further.
By the end of this lesson, you should be able to
|
explain, using examples, why order is or is not important when solving problems that involve permutations or combinations |
|
|
determine the number of combinations of n elements taken r at a time |
|
|
generalize strategies for determining the number of combinations of n elements taken r at a time |
Use the
flowchart
to help guide you throughout this lesson.
NOTE: The formula for combinations in the flow chart has an incorrect denominator. It should be r!(n - r)!
