Permutation and Combination Worksheets - Free Printable

Here is the solution to the worksheet “Permutations and Combinations,” with a clear explanation for each scenario.

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Key Concepts:

- Permutation: An arrangement of items where order matters.
Example: Finishing positions in a race (1st, 2nd, 3rd), arranging letters, selecting officers with distinct roles.

- Combination: A selection of items where order does not matter.
Example: Choosing a committee, picking fruits from a basket, selecting cards from a deck without regard to order.

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Problem Solutions:

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#### 1) During the final round of the formula one grand prix, six cars were closing in on the finish line. The top three winners were awarded gold, silver, and bronze medals.

✔ Answer: Permutation

Explanation:
The medals are distinct — gold (1st place), silver (2nd place), bronze (3rd place). The *order* in which the cars finish matters because each position gets a different medal. So we are arranging 3 cars out of 6 in a specific order → Permutation.

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#### 2) Alice places five apples, three oranges and ten peaches in a fruit basket. Her son, Brian, selects three fruits from the basket.

✔ Answer: Combination

Explanation:
Brian is just *selecting* three fruits. It doesn’t matter which fruit he picks first, second, or third — only *which three fruits* he ends up with. Order of selection doesn’t matter → Combination.

*(Note: Even though there are multiple types of fruit, the problem doesn’t specify that he’s choosing by type or order — it’s simply selecting 3 fruits.)*

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#### 3) Vanessa chooses a combination of four digits from 0 to 9 without repetition for her school locker.

✔ Answer: Permutation

Explanation:
Even though the word “combination” appears in the sentence, this is a trick! In reality, a locker code like “1-2-3-4” is different from “4-3-2-1”. The *order* of the digits matters. So even if she calls it a “combination,” mathematically, it’s a permutation.

> 💡 Fun fact: In real life, people say “combination lock,” but mathematically, it should be called a “permutation lock”!

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#### 4) Derek shuffled a pack of 52 playing cards and asked his friend, Ian, to choose any three cards.

✔ Answer: Combination

Explanation:
Ian is just choosing 3 cards — the order in which he picks them doesn’t matter. Whether he picks the Ace of Spades first or last, as long as he ends up with those 3 cards, it’s the same selection. So this is a combination.

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#### 5) Stephanie rearranged the letters in the word “TOGETHER” and formed new words beginning with R and ending with T.

✔ Answer: Permutation

Explanation:
She is *rearranging* the letters — that means changing their order. Also, the condition “beginning with R and ending with T” implies that position matters. Since the arrangement of letters creates different “words” (even if not real ones), and position is key, this is a permutation.

*(Note: We’re not just selecting letters — we’re arranging them in specific positions.)*

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✔ Final Answers:

1. Permutation
2. Combination
3. Permutation
4. Combination
5. Permutation

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Let me know if you’d like the actual formulas or calculations for any of these!