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Card duplication counting

Counting duplicate options in a group of cards

This math skill teaches how to count the number of ways to arrange a group of duplicate items while keeping them in a certain order. Here, it focuses on finding different sequences for repeated elements using factorial notation to simplify calculations.

Learn card duplication counting

Teaching Transcript

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Let's find how many ways we can organize these cards with them remaining in increasing order

We'll need to focus on the 5s in the middle as those are the duplicates, so how many ways can we order the 3 cards that are 5s?

There are 3 choices for our first 5.

For each of those 3 options for the first card, we have 2 left as options for the second card, so we multiply by 2

For each of those 2 options, however, we only have a single option left for the final card.

This can be written in shorter form by writing just 3 factorial

And if we multiply it out, our answer is that there are 6 ways of ordering the cards

Skill Practice

Counting duplicate options in a group of cards

Test your understanding of card duplication counting by practicing it! Work through the below exercises to use it in practice.