MathDB
Wot n' Binomial Notation

Source: 2017 AIME I #7

March 8, 2017
2017 AIME IWot n

Problem Statement

For nonnegative integers aa and bb with a+b≤6a + b \leq 6, let T(a,b)=(6a)(6b)(6a+b)T(a, b) = \binom{6}{a} \binom{6}{b} \binom{6}{a + b}. Let SS denote the sum of all T(a,b)T(a, b), where aa and bb are nonnegative integers with a+b≤6a + b \leq 6. Find the remainder when SS is divided by 10001000.
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