+201 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.)
+201 I believe ive done this problem before, but I might have forgotten the approach :(. All I need is a push on how to start. Thanks!
+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.)
It is very easy to double count in these questions so do not assume mine is fully correct.
| people in each team | no of ways to sort the people | ways to sort into teams | |
|---|---|---|---|
| 006 | 1 | 3 | 1*3=3 |
| 015 | 6 ways to chose the separated one | 3*2=6 | 6*6=36 |
| 024 | 6C2=15 ways to chose the separated two | 3*2=6 | 15*6=90 |
| 033 | 6C3=20 ways to separate the threes | 3*2=6 | 20*6=120 |
| 114 | 6C4=15 | 3*2=6 | 90 |
| 123 | 3*6C3=60 | 6 | 360 |
| 222 | 6*4C2=36 | 6 | 216 |
| SUM | 915 ways |
+118687 Please let me know if this agrees with any 'correct' answer you may be given.
I like to learn and improve my understanding here as well.
I put 'correct' in quotations because I would want to see the logic behind it before I would necessarily accept an alternate solution as the better or correct one.
