Where is combinations hiding in Pokémon team building?

Quick answer

Combinations help you figure out how many different Pokémon teams you can make when choosing from a group of Pokémon. It's like finding all the ways to pick your favourite Pokémon to build the best team for battles!

Learning outcome

By the end of this page, you will be able to find how many different combinations of Pokémon you can make when choosing a certain number from a larger group.

• You can choose 3 Pokémon from a group of 5 and count how many different teams you can make.
• You can compare which Pokémon combinations are the best for different battles.
• You can use simple maths to plan your Pokémon team.
• You can explain how combinations help you make smart choices.

Why this matters

Combinations are useful in many parts of life, not just Pokémon! When you're choosing which friends to invite to a party, deciding what to wear, or even planning your lunch, you're using combinations. In Pokémon, combinations help you build the strongest team by choosing the right Pokémon to battle.

Learning about combinations helps you think more carefully about choices and makes you better at planning. It's a skill you’ll use in school, games, and real life.

How it works

Combinations are all about picking items from a group where the order doesn’t matter. If you pick Pokémon A, B, and C, it's the same team as B, A, and C.

Here’s how to think about combinations:

1. Decide how many Pokémon you want to choose.
2. Decide how many Pokémon you have to choose from.
3. Use a simple method to count how many different teams you can make.

Let’s use a simple example to show how this works.

Examples you can see

Imagine you have 4 Pokémon: Charmander, Bulbasaur, Squirtle, and Pikachu.

You want to choose 2 Pokémon to make a team. How many different teams can you make?

Let’s list them:

• Charmander and Bulbasaur
• Charmander and Squirtle
• Charmander and Pikachu
• Bulbasaur and Squirtle
• Bulbasaur and Pikachu
• Squirtle and Pikachu

There are 6 different teams you can make.

You can also use a formula to count combinations:

Number of combinations = n! / (r! × (n - r)!)

Where:

• n = total number of Pokémon
• r = number of Pokémon you want to pick

For our example:

• n = 4
• r = 2

So: 4! / (2! × (4 - 2)!) = 24 / (2 × 2) = 24 / 4 = 6

That matches our list!

Try it as a mini adventure

Imagine you’re a Pokémon trainer going on a quest to build the perfect team. You have 6 Pokémon to choose from:

• Charizard
• Pikachu
• Alakazam
• Gengar
• Mewtwo
• Snorlax

Your quest is to pick 3 Pokémon to make your team. How many different teams can you make?

Let’s work it out together!

Step 1: Count how many Pokémon you have: 6 Pokémon

Step 2: Decide how many you want to pick: 3 Pokémon

Step 3: Use the formula:

6! / (3! × (6 - 3)!) = 720 / (6 × 6) = 720 / 36 = 20

So, you can make 20 different teams!

Can you imagine all 20 teams? Maybe you’ll pick your top 3 and write them down. This is like a treasure hunt for the best Pokémon combinations!

Common mistakes

• Mistake: Thinking that the order matters, like choosing Pikachu then Charizard is different from Charizard then Pikachu.
• Why it happens: It’s easy to forget that in combinations, the order doesn’t matter.
• Fix: Remember that a team of Pikachu and Charizard is the same as a team of Charizard and Pikachu.

• Mistake: Using the wrong formula or forgetting to use factorials.
• Why it happens: The formula looks tricky at first, but it’s just a way to count without listing everything.
• Fix: Start by listing small examples, then move to the formula.

• Mistake: Forgetting to check if you’ve counted all combinations.
• Why it happens: When you’re excited about Pokémon, it’s easy to miss one!
• Fix: Use a methodical way to list them, like alphabetical order or by Pokémon type.

Parent and carer guide

As a parent or carer, you can help your child learn about combinations by:

1. Using a simple example like choosing 2 Pokémon from 4 to show how combinations work.
2. Letting your child draw Pokémon or use toys to act out different teams.
3. Encouraging them to list combinations to check they’ve got all the answers.
4. Playing a game where you pick 3 Pokémon from a group and count how many teams you can make.
5. Reinforcing that combinations are about choosing, not ordering.

Don’t worry if your child makes a mistake. It’s part of learning. The key is to keep trying and to talk about what they’re doing.

Practice questions

1. How many different teams can you make if you choose 2 Pokémon from 5?
2. How many different teams can you make if you choose 3 Pokémon from 6?
3. If you have 4 Pokémon and want to make teams of 2, how many teams are there?
4. You have 7 Pokémon and want to pick 3 for your team. How many combinations?
5. How many combinations are there if you choose 4 Pokémon from 8?

Answers:

1. 10 combinations
2. 20 combinations
3. 6 combinations
4. 35 combinations
5. 70 combinations

FAQ

What is a combination?

A combination is a way to choose items from a group where the order doesn’t matter. For example, choosing Pikachu and Charizard is the same as choosing Charizard and Pikachu.

Why do we use combinations in Pokémon?

Combinations help us find all the possible teams we can make. This helps trainers plan the best Pokémon for different battles.

Can I use combinations for other things?

Yes! You can use combinations to choose friends for a game, pick toppings for pizza, or decide what to wear.

How do I know if I’ve counted all combinations?

Use a system like listing them in order or grouping them by type. This helps you make sure you don’t miss any.

Do I need to know the formula to use combinations?

No, you can start by listing small examples. The formula is helpful for bigger numbers but not needed for small ones.