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.)
+23252 006 015 024 033 042 051 060
105 114 123 132 141 150
204 213 222 231 241
303 312 321 330
402 411 420
501 510
600
+37153 Hey Geno.... I am not sure what this means.... can you explain it to me?
+23252 Let the first number in each triplet to be the number of friends on the basketball team,
the second number to be the number on the soccer team, and the third number
to be the number on the track team.
So, "015" means that there are 0 persons on the basketball team,
1 person on the soccer team, and 5 on the track team.
Since I did not assume that the friends are distinguishable, there are a lot more
possibilities than my answer has. Oops ...
+37153 Well.....that is pretty clear....I should have seen that ! Thnx ! ~EP
+118687 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.)
6 people into 3 groups.
6 0 0 3 * 6C6 = 3*1 = 3 ways
5 1 0 3! * 6C5 = 6*6 = 36 ways
4 2 0 3! * 6C4 =6*15 = 60 ways
4 1 1 3* 6C4 *2 =3*15*2 = 90 ways
3 3 0 3* 6C3 =3*20 = 60 ways
3 2 1 3!* 6C3 *3C2 =6*20*3 = 360 ways
2 2 2 1* 6C2 *4C2 =15*6 = 90 ways
3+36+60+90+60+360+90 = 699
I wont guarentee that it is correct though. 
