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Home » – The Hidden Function of the Fn Key You’ve Been Ignoring—Fix Your Keyboard Like a Pro! - Midis

– The Hidden Function of the Fn Key You’ve Been Ignoring—Fix Your Keyboard Like a Pro! - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Number of arrangements: $ \frac{4!}{2!1!1!} = 12 $

📌 So total: $4 \times 3 \times 2 \times 12 = 288$ — wait, that’s larger than total outcomes — contradiction.

📌 Ah! Here’s the mistake: we don’t need to choose the second and third separately. Once we pick the word that appears twice (4 choices), and the other two distinct words from the remaining 3 ( $\binom{3}{2} = 3$), the frequencies are fixed: one appears twice, two appear once, and one is unused. But in the multinomial count, we are overcounting because once we fix the repeated word and the two single words, the configuration is fully determined.

📌 So better: number of ways to assign frequencies: one category with 2, two categories with 1, one with 0.

📌 Number of ways to assign the roles:

📌 Choose which outcome occurs twice: 4 choices

📌 From remaining 3, choose 2 to occur once each: $\binom{3}{2} = 3$

📌 The last one occurs once? No — we have only four positions. If one occurs twice, two others once, that’s 2+1+1 = 4, so the fourth is covered. So the fourth outcome (the unused one) doesn’t need to be chosen — it’s determined.

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