8 students are planning on splitting up into 3 (non-empty) study groups. How many ways can they split up into these study groups?

Note: It is possible that a study group contains only 1 person.

Guest Dec 17, 2019

#2**+1 **

Thanks answering Guest.

8 students are planning on splitting up into 3 (non-empty) study groups. How many ways can they split up into these study groups?

Note: It is possible that a study group contains only 1 person.

8 Students

If only the number of students in each group counts then

S*S*S*S*S*S*S*S chose 3 stars from the 7 = 7C2 = 21 ways

(This is the same answer as guest got )

OR

If the exact students in each group is important then:

1,1,6 8C6 = 28

1,2,5 8C5*3 = 168

1,3,4 8C4*4 = 280

2,2,4 8C4*4C2 = 420

2,3,3 8C3*5C3 = 560

28+168+280+420+560 = 1456 ways

The first option looks right to me. The second one I am much less sure about.

No guarentees for either.

**Asker guest: If you have a number answer can you please share it with the rest of us.**

**(If you believe it to be wrong please say why you think so.)**

Melody Dec 17, 2019