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Spelling with duplicate letters

Counting multiple ways to spell a word with duplicate letter tiles

This math skill involves calculating the number of ways to arrange a word using letter tiles where some letters are duplicated. By using factorials, where each factorial represents possible arrangements of duplicate letters, the total arrangements are computed by multiplying these factorials.

Learn spelling with duplicate letters

Teaching Transcript

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How many ways can we spell the word 'heeded' with these letter tiles?

The interesting part is the duplicates, we have 3 letter tiles that are 'E's, and we have 2 letter tiles for the letter 'D'

Looking at the 'E' tiles, we have 3 options for the first tile, then for each of those, 2 for the second, and 1 for the third.

This is, in shorter form, 3 factorial

Then, looking at the 'D' tiles, we have 2 options for the first tile and then for each of those just 1 for the second.

Which is 2 factorial, if we write it in that notation

So our total number of ways of writing 'heeded' is 3 factorial, multiplied by 2 factorial

Which, when we work it out, is 12 ways to spell our word.

Skill Practice

Counting multiple ways to spell a word with duplicate letter tiles

Test your understanding of spelling with duplicate letters by practicing it! Work through the below exercises to use it in practice.