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Home » Velocity is the derivative of position, \( v(t) = \fracdsdt \). - AMAZONAWS

Velocity is the derivative of position, \( v(t) = \fracdsdt \). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 How many 8-digit positive integers have all digits either 3 or 4, and have exactly three consecutive 3's?

📌 To solve this, we can use a combinatorial approach. We want to form an 8-digit number using the digits 3 and 4, with exactly three consecutive 3's. Let's break it down:

📌 Position the block of three consecutive 3's:

📌 The block "333" can start at positions 1 through 6 in the 8-digit number. This gives us 6 possible positions for the block.

📌 Fill the remaining 5 positions:

📌 After placing "333", we have 5 positions left. Each of these can be either a 3 or a 4, except that no additional block of three consecutive 3's is allowed. We need to ensure that no new block of three consecutive 3's is formed.

📌 Count valid configurations for each block position:

📌 If "333" starts at position 1:

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