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.
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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.
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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.
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For the first letter tile, we have 5 options as it can be any of the letter tiles.
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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.
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Now, for each of those second letter tiles, we have 3 remaining options that we can use for the third letter tile.
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For each of those third letter tiles, we have 2 remaining options that we can use for the fourth letter tile
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For each of those fourth letter tiles, there is only 1 option remaining for our last letter tile.
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This form, multiplying by a sequence of decreasing numbers is called a factorial. So we have 5 factorial.
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If we multiply these out, we have 120 distinct ways to order our letter tiles.