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 ?

Solution:

Total no. of friends = 6

No. of teams = 3

No. 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)

$=(1\times^5C_1+^4C_2+^2C_2)+(1\times^5C_2+^4C_2+^2C_2) \\=(5+6+1)+(10+6+1) \\=12+17 \\=29$