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.
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.)