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Order letter tiles

Counting ways to order letter tiles without duplicates

This math skill teaches how to calculate the number of distinct ways to order a set of unique letter tiles. It explains using the factorial method, where you multiply decreasing integers corresponding to each position's available choices.

Learn order letter tiles

Teaching Transcript

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How many distinct ways can we order these letter tiles? We have 5 letter tiles and none of them are duplicates.

For the first letter tile, we have 5 options as it can be any of the letter tiles.

For each of those first letter tiles, we then have 4 options for the second letter tile, because one letter tile has already been set as the first letter tile.

Now, for each of those second letter tiles, we have 3 remaining options that we can use for the third letter tile.

For each of those third letter tiles, we have 2 remaining options that we can use for the fourth letter tile

For each of those fourth letter tiles, there is only 1 option remaining for our last letter tile.

This form, multiplying by a sequence of decreasing numbers is called a factorial. So we have 5 factorial.

If we multiply these out, we have 120 distinct ways to order our letter tiles.

Skill Practice

Counting ways to order letter tiles without duplicates

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