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.)

Guest Feb 28, 2022

#1**+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

geno3141 Feb 28, 2022

#2**+1 **

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

ElectricPavlov
Feb 28, 2022

#3**+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

#4**+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.

Melody Feb 28, 2022