How many ways are there to divide a group of 6 friends among the basketball team, the soccer team, and the track team? (Each team could have anywhere from 0 to 6 of the friends on it. Assume the friends are distinguishable.)
+118658 How many ways are there to divide a group of 6 friends among the basketball team, the soccer team, and the track team? (Each team could have anywhere from 0 to 6 of the friends on it. Assume the friends are distinguishable.)
Possibilities
0,0,6 1 way to seperate. 3 alternatives for teams =3
0,1,5 6C1 way to seperate. 3! alternatives for teams =36
0,2,4 6C2 way to seperate. 3! alternatives for teams =36
0,3,3 6C3/2 way to seperate. 3! alternatives for teams =18
1,1,4 6C4 way to seperate. 3! alternatives for teams =90
1,2,3 6C3*3 way to seperate. 3! alternatives for teams =360
2,2,2 6C2*4C2/6 way to seperate. 3! alternatives for teams =90
3+36+36+18+90+360+90 = 633
I could easily have made a mistake. If you get the correct answer, please share it here.
