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VMO 2022 problem 6 day 2

Source: Vietnam Mathematical Olympiad problem 6 day 2

March 5, 2022
vmocombinatoricsprobability

Problem Statement

We are given 4 similar dices. Denote xi(1≤xi≤6)x_i (1\le x_i \le 6) be the number of dots on a face appearing on the ii-th dice 1≤i≤41\le i \le 4 a) Find the numbers of (x1,x2,x3,x4)(x_1,x_2,x_3,x_4) b) Find the probability that there is a number xjx_j such that xjx_j is equal to the sum of the other 3 numbers c) Find the probability that we can divide x1,x2,x3,x4x_1,x_2,x_3,x_4 into 2 groups has the same sum
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