MathCastle
Counting & ProbabilitySuperchallengeBinomial Theorem, Pascal & Combinatorial Identities

Binomial Theorem, Pascal & Combinatorial Identities · Superchallenge problem

Evaluate ∑0≤i<j≤10(10i)(10j)\displaystyle\sum_{0\le i<j\le 10}\binom{10}{i}\binom{10}{j}, the sum over all pairs of integers (i,j)(i,j) with 0≤i<j≤100\le i<j\le10.