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Home » \textTotal ways = \binom153 = 455 - ClickBalance

\textTotal ways = \binom153 = 455 - ClickBalance

📅 May 17, 2026 👤 scraface

May 17, 2026

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Change variable: let $ s = v - u $, so $ v = u + s $, $ 0 \leq s \leq...
But since $ u \leq 1 - s \leq 1 $, and $ s \leq 0.2 $, the upper limit...
\int_0^1 \int_0^{\min(0.2, 1 - u)} 30 s^4 \, ds \, du
Split into two regions: $ 0 \leq u \leq 0.8 $, where $ 1 - u \geq 0.2...
= \int_0^{0.8} \int_0^{0.2} 30 s^4 ds \, du + \int_{0.8}^1 \int_0^{1 -...
First integral:
\int_0^{0.2} 30 \cdot \frac{s^5}{5} ds = 6 \int_0^{0.2} s^5 ds = 6 \cd...
Multiply by 1 (no outer u): $ \frac{1}{15625} $
Second integral:
\int_{0.8}^1 30 \cdot \frac{(1 - u)^5}{5} du = 6 \int_{0.8}^1 (1 - u)^...

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