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📅 May 2, 2026 👤 scraface

May 02, 2026

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🔥 Popular Posts

Question:** A youth mentorship program has 10 students and 6 mentors....
This is a classic surjective mapping problem: assigning 10 distinguish...
This is the number of **onto** functions from a 10-element set to a 6-...
\sum_{k=0}^{6} (-1)^k \binom{6}{k} (6 - k)^{10}
This uses the inclusion-exclusion principle:
$ k = 0 $: $ \binom{6}{0} \cdot 6^{10} = 1 \cdot 60466176 = 60466176 $
$ k = 1 $: $ -\binom{6}{1} \cdot 5^{10} = -6 \cdot 9765625 = -58593750...
$ k = 2 $: $ \binom{6}{2} \cdot 4^{10} = 15 \cdot 1048576 = 15728640 $
$ k = 3 $: $ -\binom{6}{3} \cdot 3^{10} = -20 \cdot 59049 = -1180980 $
$ k = 4 $: $ \binom{6}{4} \cdot 2^{10} = 15 \cdot 1024 = 15360 $

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