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Home » A_B = 1000(1.04)^t - RedTag Digital

A_B = 1000(1.04)^t - RedTag Digital

📅 May 17, 2026 👤 scraface

May 17, 2026

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This is a classic inclusion-exclusion problem. The total number of ass...
Let $ A_i $ be the set of assignments where device $i$ is not used, fo...
Then the number of onto functions is:
\sum_{k=0}^{5} (-1)^k \binom{5}{k} (5 - k)^8
$ k = 0 $: $ (-1)^0 \binom{5}{0} \cdot 5^8 = 1 \cdot 1 \cdot 390625 =...
$ k = 1 $: $ (-1)^1 \binom{5}{1} \cdot 4^8 = -1 \cdot 5 \cdot 65536 =...
$ k = 2 $: $ (-1)^2 \binom{5}{2} \cdot 3^8 = 1 \cdot 10 \cdot 6561 = 6...
$ k = 3 $: $ (-1)^3 \binom{5}{3} \cdot 2^8 = -1 \cdot 10 \cdot 256 = -...
$ k = 4 $: $ (-1)^4 \binom{5}{4} \cdot 1^8 = 1 \cdot 5 \cdot 1 = 5 $
$ k = 5 $: $ (-1)^5 \binom{5}{5} \cdot 0^8 = -1 \cdot 1 \cdot 0 = 0 $

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