Question

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!!!!!!!

Answer 1

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!