which of the following is an example of a combination

Guri Bee

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19-10-2024

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Understanding Combinations: Unlocking the Power of Choices

In mathematics, a combination refers to a selection of items from a set where the order of the items doesn't matter. Think of it as choosing a group of friends for a movie night – the order you choose them in doesn't change the group itself.

Let's dive into the world of combinations with an example from a GitHub discussion, where a user asked:

"Which of the following is an example of a combination?"

Option A: Selecting a team of 5 players from a group of 12.

Option B: Arranging 7 books on a shelf.

Option C: Choosing a president, vice president, and treasurer from a pool of 10 candidates.

The Correct Answer: Option A is an example of a combination.

Why?

• Option A: Choosing a team of 5 players from 12 doesn't care about the order you select them in. The team remains the same whether you pick player A then B then C, or C then B then A.

• Option B: Arranging books on a shelf is a permutation, where order matters. Changing the order of the books creates a different arrangement.

• Option C: Choosing a president, vice president, and treasurer is also a permutation because the order of selection determines the roles. Picking Candidate X as president and Candidate Y as vice president is different from picking Candidate Y as president and Candidate X as vice president.

Practical Examples of Combinations

• Choosing ingredients for a pizza: Whether you pick pepperoni first or mushrooms first, the final pizza is the same.
• Selecting lottery numbers: The order you choose the numbers doesn't matter; the winning combination is the same regardless of the order.
• Picking a hand of cards: A hand of 5 cards is the same regardless of the order they were dealt.

Key Takeaway:

Combinations are all about selecting a group where the order of selection doesn't change the outcome. Remember to consider the nature of the problem to determine whether order matters – if it does, you're dealing with a permutation.