Missing all four letters: impossible, so 0. - United Radiology

April 22, 2026 · United Radiology

Missing all four letters: impossible, so 0. - United Radiology

Missing All Four Letters: Impossible, So 0
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Why would someone talk about “missing all four letters: impossible, so 0” in a digital age defined by data compression and hidden meanings?

Missing all four letters: impossible, so 0. - United Radiology

Missing all four letters: impossible, so 0. - United Radiology

Missing all four letters: impossible, so 0. - United Radiology

Missing all four letters: impossible, so 0. - United Radiology

Missing all four letters: impossible, so 0. - United Radiology

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Solution: We are to count the number of 5-character strings using the letters A, B, C, D (4 letters), such that each letter appears at least once. This is a classic inclusion-exclusion problem.

Solution: We are to count the number of 5-character strings using the letters A, B, C, D (4 letters), such that each letter appears at least once. This is a classic inclusion-exclusion problem.

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We first compute the total number of strings of length 5 using 4 letters:

We first compute the total number of strings of length 5 using 4 letters:

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Now subtract the strings that miss at least one letter. Let $ S $ be the set of all such strings, and for each letter, let $ A_i $ be the set of strings that do not contain letter $ i $. We want:

Now subtract the strings that miss at least one letter. Let $ S $ be the set of all such strings, and for each letter, let $ A_i $ be the set of strings that do not contain letter $ i $. We want:

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Alternatively, since there are 4 letters and we require each to appear at least once in 5 positions, exactly one letter appears twice, and the others once.

Alternatively, since there are 4 letters and we require each to appear at least once in 5 positions, exactly one letter appears twice, and the others once.

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Assign the remaining 3 letters to the 3 positions (in $ 3! = 6 $ ways)

Assign the remaining 3 letters to the 3 positions (in $ 3! = 6 $ ways)

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Count how many integers fall in each residue class:

Count how many integers fall in each residue class:

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