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.)

jxc516 Feb 28, 2021

#3**+2 **

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!

jxc516 Mar 1, 2021

#4**+3 **

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 |

Melody Mar 1, 2021

#5

#6**0 **

**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.

Melody
Mar 2, 2021