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# help

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+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.)

Feb 28, 2021

#1
+113132
0

Mar 1, 2021
#2
+201
+2

Replied

Thanks! :)

jxc516  Mar 1, 2021
#3
+201
+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!

Mar 1, 2021
#4
+113132
+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
Mar 1, 2021
#5
+201
+3

Thank you!

Mar 1, 2021
#6
+113132
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