Topic
Volleyball tournament includes 9 participating teams, including 3 teams from country X. The organizers randomly draw teams to place teams into 3 groups A, B, C and each group has 3 teams. Calculate the number of ways to arrange the 3 teams of country X in 3 different tables.
Solution method – See details
Actions are performed in consecutive steps
Step 1: Calculate the number of ways to select 3 teams into Group A (in which 1 team from country X is selected)
Step 2: Calculate the number of ways to select 3 teams from the remaining 6 teams into Group B, in which 1 team of country X is selected from the remaining 2 teams of country X (the last 3 teams are obviously placed in Group C)
Step 3: Apply the multiplication rule to calculate the number of satisfying choices
Detailed explanation
According to the topic, the 9 participating teams include 3 teams from country X and 6 teams from other countries
+) Number of ways to choose 3 teams to be placed in Group A, including 1 team from country X is: \(C_3^1.C_6^2\) = 45 ways
+) The number of ways to choose 3 teams from the remaining 6 teams to be placed in Group B, including 1 team from country X is: \(C_2^1.C_4^2 = 12\)how to choose
+) Obviously the last 3 teams will be placed in Group B
So the number of ways to arrange such that the 3 teams of country X in 3 different tables are: 45.12 = 540 ways to satisfy the arrangement.
