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# Probability

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260
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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, 2022

#1
+23239
+1

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

Feb 28, 2022
#2
+36721
+1

Hey Geno....  I am not sure what this means.... can you explain it to me?

ElectricPavlov  Feb 28, 2022
#3
+23239
+1

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 ...

geno3141  Feb 28, 2022
#5
+36721
0

Well.....that is pretty clear....I should have seen that !    Thnx !     ~EP

ElectricPavlov  Feb 28, 2022
#4
+118577
+1

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.

Feb 28, 2022
edited by Melody  Feb 28, 2022