We are given 4 similar dices. Denote $x_i (1\le x_i \le 6)$ be the number of dots on a face appearing on the $i$-th dice $1\le i \le 4$ a) Find the numbers of $(x_1,x_2,x_3,x_4)$ b) Find the probability that there is a number $x_j$ such that $x_j$ is equal to the sum of the other 3 numbers c) Find the probability that we can divide $x_1,x_2,x_3,x_4$ into 2 groups has the same sum
Problem
Source: Vietnam Mathematical Olympiad problem 6 day 2
Tags: vmo, combinatorics, probability
799786
05.03.2022 10:50
I don't know why this year the combinatoric problem is easy.
And also, there is only one combinatoric problem. Sad
aves
05.03.2022 17:09
wardtnt1234 wrote:
I don't know why this year the combinatoric problem is easy.
And also, there is only one combinatoric problem. Sad
yeah, grade 10 can solve this problem well
aves
05.03.2022 17:13
wardtnt1234 wrote: We are given 4 similar dices. Denote $x_i (1\le x_i \le 6)$ be the number of dots on a face appearing on the $i$-th dice $1\le i \le 4$ a) Find the numbers of $(x_1,x_2,x_3,x_4)$ b) Find the probability that there is a number $x_j$ such that $x_j$ is equal to the sum of the other 3 numbers c) Find the probability that we can divide $x_1,x_2,x_3,x_4$ into 2 groups has the same sum any hints for problem $c$?
aves
05.03.2022 18:02
a) $6^4$ b) $\frac{5}{81}$