I'm sorry for asking a question that has already been asked, but the last time this was posted, it did not get good answers. Please help me!:

It is a beautiful day at the beach and ten beach volleyball players have shown up at the volleyball courts. 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 ways can a two-person team be assembled such that no player feels out of position?

BigBoiChungus Jun 26, 2021

#1**+4 **

Is it okay if I answer?

Spikers = 5, Setters = 4 and 1 either way.

Each 2-person team should have 1 setter and 1 spiker.

**Case 1**** : **If spikers = 6 and setters = 4 **Case 2 : **If spikers = 5 and setters = 5

Then no. of ways \(={^6} C_{1}×{^4}C_{1}\) Then no. of ways \(={^5} C_{1}×{^5}C_{1}\)

In order to get total no. of ways, add the respective values you get in both cases.

amygdaleon305 Jun 26, 2021

#1**+4 **

Best Answer

Is it okay if I answer?

Spikers = 5, Setters = 4 and 1 either way.

Each 2-person team should have 1 setter and 1 spiker.

**Case 1**** : **If spikers = 6 and setters = 4 **Case 2 : **If spikers = 5 and setters = 5

Then no. of ways \(={^6} C_{1}×{^4}C_{1}\) Then no. of ways \(={^5} C_{1}×{^5}C_{1}\)

In order to get total no. of ways, add the respective values you get in both cases.

amygdaleon305 Jun 26, 2021