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.
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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.
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Let's find how many ways we can organize these cards with them remaining in increasing order
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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?
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There are 3 choices for our first 5.
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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
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For each of those 2 options, however, we only have a single option left for the final card.
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This can be written in shorter form by writing just 3 factorial
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And if we multiply it out, our answer is that there are 6 ways of ordering the cards