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Order cards

Counting ways to order a hand of cards without duplicates

The math skill demonstrated teaches how to calculate the number of distinct ways to order a set of unique items (cards) using factorial calculation. It explains decremental multiplication for each successive choice, illustrating the concept of factorial.

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Teaching Transcript

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How many distinct ways can we order these cards? We have 4 cards and none of them are duplicates.

For the first card, we have 4 options as it can be any of the cards.

For each of those first cards, we then have 3 options for the second card, because one card has already been set as the first card.

Now, for each of those second cards, we have 2 remaining options that we can use for the third card.

For each of those third cards, there is only 1 option remaining for our last card.

This form, multiplying by a sequence of decreasing numbers is called a factorial. So we have 4 factorial.

If we multiply these out, we have 24 distinct ways to order our cards.

Skill Practice

Counting ways to order a hand of cards without duplicates

Test your understanding of order cards by practicing it! Work through the below exercises to use it in practice.