MathCastle
Counting & ProbabilitySuperchallengeIdentities and Techniques, Proved

Identities and Techniques, Proved · Superchallenge problem

Evaluate ∑k=010(−1)k(10k)(22−k12)\displaystyle\sum_{k=0}^{10}(-1)^k\binom{10}{k}\binom{22-k}{12}.