Permutations and Combinations Notes and Worksheets - Lindsay Bowden - Free Printable

Here are the answers to fill in your notes and solve the examples.

Part 1: Definitions (The Notes Section)

Here is how to fill in the blanks for the definitions at the top of the page:

* outcome – the result of an experiment or event
* permutation – a way to find the number of arrangements where order DOES matter
* combination – a way to find the number of groups (or selections) where order DOES NOT matter
* factorial – the product of a number and all whole numbers below it
* *Ex: 5! =* $5 \times 4 \times 3 \times 2 \times 1 = 120$

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Part 2: Examples (Permutation or Combination?)

Here is the breakdown for each example problem. The key is to ask yourself: "Does the order change the result?"

1. Ways to arrange the 6 numbers that open a locker
* Answer: Permutation
* *Why:* If your code is 1-2-3, entering 3-2-1 won't open the locker. The specific order matters.

2. Number of different types of sandwiches you can make with these ingredients: ham, turkey, white bread, wheat bread, lettuce, tomato
* Answer: Combination
* *Why:* A sandwich with ham on white bread is the same as a sandwich with white bread and ham. The order you pile the ingredients doesn't change what kind of sandwich it is; only which ingredients you chose matters.

3. Ways to arrange books on a shelf
* Answer: Permutation
* *Why:* Putting Book A first and Book B second looks different than putting Book B first and Book A second. The arrangement matters.

4. The number of ways the letters in the word HORSE can be arranged
* Answer: Permutation
* *Why:* Changing the order of the letters creates a different arrangement (like H-O-R-S-E vs. E-S-R-O-H).

5. Possible winners when drawing 3 names from a box of 10 names
* Answer: Combination
* *Why:* Usually, when you just draw "winners," they all get the same prize. It doesn't matter if you were drawn first or last; you still win. The group of people matters, not the order they were picked.

6. Ways to arrange the 1st, 2nd, and 3rd place winners in a game
* Answer: Permutation
* *Why:* Winning 1st place is very different from winning 3rd place. The specific position (order) matters.

7. Possible lottery winners when drawing 6 numbers from a pool of 50 numbers
* Answer: Combination
* *Why:* In most lotteries, if the winning numbers are 5, 10, 15, 20, 25, 30, your ticket wins even if you wrote them down in a different order (like 30, 25, 20...). Only the group of numbers matters.

8. Possible 4-digit codes for a home security system
* Answer: Permutation
* *Why:* Just like the locker, the code 1-2-3-4 is different from 4-3-2-1. The order must be exact to work.

9. Possible license plates with 6 letters and numbers
* Answer: Permutation
* *Why:* A license plate reading "ABC-123" is a completely different car registration than "CBA-321". The order of the characters defines the plate.

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Final Answer:

Definitions:
* outcome: result
* permutation: arrangements, matter
* combination: groups, matter
* factorial: product, whole numbers
* Ex: 5! = 120

Examples:
1. Permutation
2. Combination
3. Permutation
4. Permutation
5. Combination
6. Permutation
7. Combination
8. Permutation
9. Permutation