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Order letter tiles with repeats

Counting ways to order letter tiles with duplicates

This math skill involves calculating the number of distinct ways to order a set of letter tiles when some tiles are duplicates. It teaches calculating the total permutations of all tiles and then dividing by the permutations of the duplicate tiles to ensure each configuration is unique.

Learn order letter tiles with repeats

Teaching Transcript

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How many distinct ways can we order these letter tiles? We have 5 letter tiles, but 2 of them are duplicates

We can calculate all the ways of ordering the letter tiles, ignoring the duplicates, and then divide that by the number of ways that duplicates can be created

Looking at all the possibilities, we have 5 options for the first letter tile, and for each of those, 4 options for the second letter tile, and so on.

For the duplicates, there are two ways that a double letter can be arrange and still be identical.

We a factorial pattern. We have 5 factorial, divided by 2 factorial.

Cancelling like terms on top and bottom, we are left with 5 times 4 times 3. So we have a total of 60 distinct ways to order this set of letter tiles

Skill Practice

Counting ways to order letter tiles with duplicates

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