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Home » Finally Away from Sticky Keys! Master This Fast Troubleshooting Step-by-Step - Treasure Valley Movers

Finally Away from Sticky Keys! Master This Fast Troubleshooting Step-by-Step - Treasure Valley Movers

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 We can fix the positions of the 2 R’s, 2 L’s, and 1 T, then impose the constraint that the largest R index < smallest L index.

📌 But a more efficient method: consider the relative order of the R’s and L’s only.

📌 There are \(\binom{4}{2} = 6\) ways to place the two R’s in 4 slots (the other two are for L’s); the rest go to L’s. But since L’s are indistinct, each such placement defines a relative order.

📌 Only one of these 6 corresponds to both R’s before both L’s: R R L L.

📌 Thus, only **1** out of the \(\binom{4}{2} = 6\) ways to interleave R’s and L’s satisfies the condition.

📌 But these 6 interleavings are not equally likely when indistinguishable — actually, the number of distinct sequences where both R’s precede both L’s is equal to the number of ways to choose 2 positions for R’s such that both are before the positions of both L’s.

📌 Fix the positions: choose 2 out of 5 for R’s, 2 for L’s, 1 for T. Total: \(\binom{5}{2,2,1} = \frac{5!}{2!2!1!} = 30\), as before.

📌 Now count how many of these 30 have both R positions less than both L positions.

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