There are ten volleyball players. Each two-person volleyball team should consist of a setter and a spiker. Five of the players prefer to be a spiker, four of the players prefer to be a setter, and one player is fine either way. In how many?
...In how many ways can a two-person team be assembled such that no player feels out of position?
~ Question from AoPS ~
Information Breakdown
Subject: Prealgebra
Focus: Counting Pairs
PLEASE PLEASE PLEASE HELP!!!!!!!
...In how many ways can a two-person team be assembled such that no player feels out of position?
~ Question from AoPS ~
Information Breakdown
Subject: Prealgebra
Focus: Counting Pairs
PLEASE PLEASE PLEASE HELP!!!!!!!
1 Answer
Jun 14, 2018
This is when you want to make ONE team:
Explanation:
The five spikers can each choose from 5 setters (4 setters and 1 don't care). This gives 25 combinations.
The don't care can take the role of spiker and choose from 4 setters
An other way of solving this problem:
The five spikers can each choose from 4 setters: 20 combinations.
The don't care can team up with any of the 9 others
In both cases: Grand Total = 29.
Note:
If the question were "in how many way can you make up 5 teams?" the calculation would be quite different!
