Answer to Question #248031 in Discrete Mathematics for Bvffyjfee

Question

There are 6 friends Ajay, Bob, Chintu, Devi, Emily and Fatima. They want to play a game which requires three teams. (Each team must have at least one player.) In how many ways can they form such teams if Chintu does not want to be alone in a team ?

Answer 1

Total no. of friends = 6 (Ajay, Bob, Chintu, Devi, Emily and Fatima)

Number of teams = 3

Each team must have at least one player but Chintu does not want to be alone in a team. So, total number of ways to form three teams with at least one member in a team will be:

Number of required ways to form teams = (Chintu and one player + Two other players + Two remaining players) + (Chintu and two players + Two other players + one remaining player)

= [1 * (⁵C₁ + ⁴C₂ + ²C₂) + [1 * (⁵C₂ + ⁴C₂ + ²C₂)

= (5 + 6 + 1) + (10 + 6 + 1)

= 29

This means there are total 29 ways to form three teams with at least one member in a team.